assignment 6 perimeter and area

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6.2: Perimeter and Area

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Perimeter is a one-dimensional measurement that is taken around the outside of a closed geometric shape. Let’s start our discussion of the concept of perimeter with an example.

Guided Example

Joseph does not own a car so must ride the bus or walk everywhere he goes. On Mondays, he must get to school, to work, and back home again. His route is pictured in figure 1.

The obvious question to ask in this situation is, “how many miles does Joseph travel on Mondays”? To compute, we each distance: 3 + 6 + 6 = 15.

Joseph travels 15 miles on Mondays.

Another way to work with this situation is to draw a shape that represents Joseph’s travel route and is labeled with the distance from one spot to another.

Notice that the shape made by Joseph’s route is that of a closed geometric figure with three sides (a triangle) (see figure 2). What we can ask about this shape is, “what is the perimeter of the triangle”?

Perimeter means “distance around a closed figure or shape” and to compute we add each length: 3 + 6 + 6 = 15

Our conclusion is the same as above: Joseph travels 15 miles on Mondays.

However, what we did was model the situation with a geometric shape and then apply a specific geometric concept ( perimeter ) to computer how far Joseph traveled.

Notes on Perimeter

• Perimeter is a one-dimensional measurement that represents the distance around a closed geometric figure or shape (no gaps).
• To find perimeter, add the lengths of each side of the shape.
• If there are units, include units in your final result. Units will always be of single dimension (i.e. feet, inches, yards, centimeters, etc…)

To compute perimeter, our shapes must be closed. Figure 3 shows the difference between a closed figure and an open figure.

Find the perimeter for each of the shapes below.

How do we find the perimeter of this more complicated shape?

Just keep adding those side lengths. 6 + 7 + 4 + 4 + 5 + 6 + 2 = 34 units

If you look closely at the shapes in the previous examples, you might notice some ways to write each perimeter as a more explicit formula. See if the results from what we have done so far match the formulas below.

Circumference

You may realize that we have not yet discussed the distance around a very important geometric shape: a circle! The distance around a circle has a special name called the  circumference . To find the circumference of a circle, we use this formula: C = 2πr

Let’s see where the formula for circumference comes from. Figure 4 shows a generic circle with radius r.

Notes about C = 2π r

Remember that in the formula, when computing the circumference C = 2π r , we multiply as follows usually substituting 3.14 in place of π:

C = 2 × 3.14 × r

Often, the use of ( ) will help make the different parts of the formula easier to see:

C = (2)×(3.14)×( r )

Origins of C = 2π r

We know from our previous work that to identify the unknown, C , we can move d to the other side of the equation by writing C = π d. The diameter is all the way across the circle’s middle so the diameter is twice the radius. We can update C in terms of the radius as C = π(2 r ). With a little final rearranging of the order our parts are written in, we can say that C = 2π r.

Let’s use the formula to find the circumference of a few circles.

Find the circumference of each of the following circles. Leave your answers first in exact form and then in rounded form (to the hundredths place). (Note that when a radius is given, its value is centered above a radius segment. When a diameter is given, its value is centered above a diameter segment.)

• Exact 8π in; rounded from exact answer 25.13 in; rounded using 3.14 for π 25.12 in
• Exact 12.44π m; rounded from exact answer 39.08 m; rounded using 3.14 for π 39.06 m

Exact Form vs. Rounded Form

• π is a number in exact form. It is not rounded.
• 3.14 is a rounded form approximation for π

Why does it matter which form we use? It matters because when we round, we introduce error into our final result. For this class, that error is usually acceptable. However, you will find in other subjects such as physics or chemistry, that level of accuracy is a concept of great importance. Let’s see an example of the difference in forms.

The radius of the moon is about 1079 miles. What is the circumference? Let’s solve this using both the exact form and the rounded form:

Exact Solution

To round from the exact solution, use the π button on your calculator to get

Rounded Solution

Notice that our final results are different. That difference is the error created by using 3.14 as an initial approximation for π. When doing homework and tests, read the directions carefully on each problem to see which form to use.

Find the circumference or perimeter given in each described situation below. Include a drawing of the shape with the included information. Use the examples to help determine what shapes to draw. Show all work. As in the examples, if units are included then units should be present in your final result. Round to tenths unless indicated otherwise.

• Find the perimeter of a square with side length 2.17 feet.
• Find the perimeter of a rectangle with sides of length 4.2 and 3.8.
• Find the perimeter of a triangle with sides of length 2, 5, 7.
• Find the circumference of a circle with radius 6 inches. Present answer in exact form and also compute using 3.14 for π. Present rounded form to the nearest tenth.
• Find the circumference of a circle with diameter 14.8 inches. Present answer in exact form and also compute using 3.14 for π. Present rounded form to the nearest tenth.
• Exact 12π in, Rounded 37.7 in
• Exact 14.8π in, Rounded 46.5 in

Finding the Distance around Non-Standard Shapes

The basic formulas for perimeter of straight-line shapes and the circumference of a circle will help us find the distance around more complicated figures. Find the distance around the following shape. Round final answer to tenths and use 3.14 for π.

Applications of Perimeter and Circumference

Our knowledge of basic geometric shapes can be applied to solve “real-life” problems.

Wally wants to add a fence to the back of his house to make some room for his children to play safely (see diagram below). He began measuring his yard but got distracted and forgot to finish measuring before he went to the store. If he remembers that the back wall of his house is 15 yards long, does he have enough information to buy the fencing he needs? If so, how many feet should he buy?

Let’s take another look at Wally’s backyard from Example 7 in order to introduce the next concept: area.

Wally successfully fenced his yard but now wants to add some landscaping and create a grassy area as shown below.

He heads down to the local lawn store and finds out that in order to determine how much sod he needs, he must figure out the square footage of the area he wants to add grass to. On his way home, he realizes that if he divides the grassy area into sections that are 1 foot by 1 foot and then counts them, he can determine the square footage. Here is the information Wally drew up when he got home.

Wally correctly determined the area of the rectangular grassy section to be 30 square feet.

Notes on Area

• Area is a two-dimensional measurement that represents the amount of space inside a two-dimensional shape.
• To find the area, count the number of unit squares inside the shape.
• If there are units, include units in your final result. Units will always be two-dimensional (i.e. square feet, square yards, square miles, etc…)

Find the area for each of the shapes below.

How do we find the area for shapes that are more complicated? Break up the areas into shapes that we recognize and add the area values together.

If you look closely at the shapes in the previous examples, you might notice some ways to write each area as a more explicit formula. See if the results from what we have done so far match the formulas below.

The area formulas for the shapes below are more complicated to derive so the formulas are listed for you in the table.

Find the area for each described situation. Create a drawing of the shape with the included information. Show all work. As in the examples, if units are included then units should be present in your final result. Use 3.14 for π and round answers to tenths as needed.

• Find the area of a rectangle whose length is 12.9 meters and height is one-third that amount.
• 55.5 m 2 or 55.5 square meters (rounded)
• 85.8 in 2 or 85.8 square inches (rounded)
• Exact 49/9 π in 2 , Rounded 17.1 in 2

Find the area given each described situation. Include a drawing of the shape with the included information. Show all work. As in the examples, if units are included then units should be present in your final result. Round answers to tenths unless otherwise indicated.

• Find the area of a square with side length 4.2 feet.
• Find the area of a rectangle with sides of length 4.2 and 3.8.
• Find the area of a triangle with height 7 inches and base 12 inches.
• Find the area of a circle with radius 6 inches. Present answer in exact form and also compute using 3.14 for π. Present rounded form to the nearest tenth.
• 17.64 ft 2 or 17.64 square feet
• 42 in 2 or 42 square inches
• Exact 36π in 2 or 36π square inches, Rounded using 3.14 for π 113.0 in 2 or 113.0 square inches

Finding the Area of Non-Standard Shapes

The basic formulas for area will help us find the area of more complicated figures. This is the same problem we found the perimeter for earlier. Find the area of the given shape. Compute using 3.14 for π and round to the nearest tenth.

Rounded using 3.14 for π 25.9 in 2

Applications of Area and Perimeter

We can combine our knowledge of area/perimeter to solve problems such as this one.

Wally is still fixing up his house and has a flooring project to complete. He wants to buy enough bamboo flooring to cover the floor space in rooms A, C and hallway B and enough bamboo edging for baseboards in all the spaces as well. How many square feet of flooring and how many feet of baseboards should he buy?

256 ft 2 flooring, 108 ft edging

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4.6: Area and Perimeter of Triangles

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Area is half the base times the height while the perimeter is the sum of the sides.

The formula for the area of a triangle is half the area of a parallelogram .

Area of a Triangle: \(A=\dfrac{1}{2} bh\) or \(A=\dfrac{bh}{2}\).

What if you were given a triangle and the size of its base and height? How could you find the total distance around the triangle and the amount of space it takes up?

For Examples 1 and 2, use the following triangle.

Example \(\PageIndex{1}\)

Find the height of the triangle.

Use the Pythagorean Theorem to find the height.

\(\begin{align*} 8^2+h^2 &=17^2 \\ h^2 &=225\\ h &=15 in \end{align*} \)

Example \(\PageIndex{2}\)

• Find the perimeter.

We need to find the hypotenuse. Use the Pythagorean Theorem again.

\(\begin{align*} (8+24)^2+15^2 &=h^2 \\ h^2 &=1249 \\ h &\approx 35.3 in \end{align*}\)

The perimeter is \(24+35.3+17\approx 76.3\: in\).

Example \(\PageIndex{3}\)

Find the area of the triangle.

To find the area, we need to find the height of the triangle. We are given two sides of the small right triangle , where the hypotenuse is also the short side of the obtuse triangle.

\(\begin{align*} 3^2+h^2&=5^2 \\ 9+h^2&=25 \\ h^2&=16 \\h &=4 \\ A&=\dfrac{1}{2}(4)(7)=14 \: units^2 \end{align*}\)

Example \(\PageIndex{4}\)

Find the perimeter of the triangle in Example 3.

To find the perimeter, we need to find the longest side of the obtuse triangle. If we used the black lines in the picture, we would see that the longest side is also the hypotenuse of the right triangle with legs 4 and 10.

\(\begin{align*} 4^2+10^2&=c^2 \\ 16+100&=c^2 \\ c &=\sqrt{116}\approx 10.77 \end{align*} \)

The perimeter is \(7+5+10.77\approx 22.77\) units

Example \(\PageIndex{5}\)

Find the area of a triangle with base of length \(28 \: cm\) and height of \(15\: cm\).

The area is \(dfrac{1}{2}(28)(15)=210\: cm^2\).

Use the triangle to answer the following questions.

• Find the height of the triangle by using the geometric mean.
• Find the area.

Find the area of the following shape.

• What is the height of a triangle with area \(144\: m^2\) and a base of \(24\: m\)?

In questions 6-11 we are going to derive a formula for the area of an equilateral triangle.

• What kind of triangle is \(\Delta ABD\)? Find \(AD\) and \(BD\).
• Find the area of \(\Delta ABC\).
• If each side is \(x\), what is \(AD\) and \(BD\)?
• If each side is \(x\), find the area of \(\Delta ABC\).
• Using your formula from #9, find the area of an equilateral triangle with 12 inch sides.
• Using your formula from #9, find the area of an equilateral triangle with 5 inch sides.

Review (Answers)

To see the Review answers, open this PDF file and look for section 10.3.

Additional Resources

Interactive Element

Video: Area of a Triangle (Whole Numbers)

Activities: Area and Perimeter of Triangles Discussion Questions

Study Aids: Triangles and Quadrilaterals Study Guide

Practice: Area and Perimeter of Triangles

Real World: Perimeter

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Grade 6 - Shape and Space

Standard 6.SS.3 - Calculate the area and perimeter of rectangles and squares with word problems.

Included Skills:

Develop and apply a formula for determining the: • perimeter of polygons. • area of rectangles. • volume of right rectangular prisms. • Explain, using models, how the perimeter of any polygon can be determined. • Generalize a rule (formula) for determining the perimeter of polygons, including rectangles and squares. • Explain, using models, how the area of any rectangle can be determined. • Generalize a rule (formula) for determining the area of rectangles. • Explain, using models, how the volume of any right rectangular prism can be determined. • Generalize a rule (formula) for determining the volume of right rectangular prisms. • Solve a given problem involving the perimeter of polygons, the area of rectangles and/or the volume of right rectangular prisms.

If you notice any problems, please let us know .

Area and Perimeter Worksheets Grade 6

Area and perimeter worksheets grade 6 will help students retain the concept of area and perimeter of different shapes. The area of any given figure is the space occupied by it, while the perimeter is the total length surrounding the figure. The answer key is also provided with these worksheets with step-by-step solutions provided.

Benefits of Grade 6 Area and Perimeter Worksheets

Area and perimeter worksheets grade 6 will benefit the students in identifying the different shapes and learning how the calculation of area and perimeter is different for each of them. These 6th grade math worksheets will help in building a strong base for higher geometrical studies. With a variety of questions related to the area and perimeter of the square, rectangle, rhombus, trapezium, triangles, these worksheets will give enough practice to gain confidence in geometry.

Printable PDFs for 6th Grade Area and Perimeter Worksheets

These worksheets should be practiced regularly and are free to download in PDF formats.

• Math 6th Grade Area and Perimeter Worksheet
• 6th Grade Area and Perimeter Math Worksheet
• Sixth Grade Area and Perimeter Worksheet
• Grade 6 Math Area and Perimeter Worksheet

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Perimeter and Area Worksheet for Class 6 PDF with Answers

These Perimeter and Area Worksheet for Class 6 PDF can be helpful for both teachers and students. Teachers can track their student’s performance in the chapter Perimeter and Area. Students can easily identify their strong points and weak points by solving questions from the worksheet. Accordingly, students can work on both weak points and strong points. 

All students studying in CBSE Class 6th, need to practise a lot of questions for the chapter Perimeter and Area. Students can easily practise questions from the Perimeter and Area problems worksheet PDF. By practising a lot of questions, students can improve their confidence level. With the help of confidence level, students can easily cover all the concepts included in the chapter Perimeter and Area. 

Perimeter and Area Worksheet for Class 6 with Solutions

Solutions is the written reply for all questions included in the worksheet. With the help of Perimeter and Area worksheets with solutions, students can solve all doubts regarding questions. Students can have deep learning in the chapter Perimeter and Area by solving all their doubts. By solving doubts, students can also score well in the chapter Perimeter and Area. 

Perimeter and Area Worksheet PDF

Worksheet is a sheet which includes many questions to solve for Class 6th students. The Perimeter and Area worksheet PDF provides an opportunity for students to enhance their learning skills. Through these skills, students can easily score well in the chapter Perimeter and Area. Students can solve the portable document format (PDF) of the worksheet from their own comfort zone. 

How to Download the Perimeter and Area Worksheet PDF? 

To solve questions from the Perimeter and Area Worksheet for Class 6 PDF, students can easily go through the given steps. Those steps are- 

• Open Selfstudys website.

• Bring the arrow towards CBSE which can be seen in the navigation bar. 

• Drop down menu will appear, select KVS NCERT CBSE Worksheet. 

• A new page will appear, select class 6th from the given list of classes. 
• Select Mathematics from the given list of subjects. Now click the chapter’s name that is Perimeter and Area. 

Features of the Perimeter and Area Worksheet PDF

Before starting to solve questions from the Perimeter and Area problems worksheet PDF, students need to know everything about the worksheet. Those features are- 

• Variety of questions are included:  The Perimeter and Area Maths Worksheet for Class 6 includes varieties of questions. Those varieties of questions are- one mark questions, two mark questions, three mark questions, etc. 
• Solutions are provided:  Doubts regarding each question can be easily solved through the solutions given. Through solving questions, a student's comprehensive skill can be increased. 
• All concepts are covered:  By solving questions from the Perimeter and Area problems worksheet, students can easily cover all the concepts included in the chapter.  
• Created by Expert:  These worksheets are personally created by the subject experts. These Perimeter and Area worksheet pdf are created with proper research. 
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Students are requested to follow some tips to score good marks in the Perimeter and Area Worksheet for Class 6. Those tips are-

• Complete all the concepts:  First and the most crucial step is to understand all the concepts included in the chapter Perimeter and Area.  
• Practise questions:  Next step is to practise questions from the Perimeter and Area problems worksheet. Through this students can identify all types of questions: easy, moderate, difficult, etc.  
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Students studying in Class 6 should start solving worksheets after covering each and every concept included in the chapter. Regular solving questions from the Perimeter and Area worksheet PDF, can help students to have a better understanding of the chapter. Better understanding of the chapter Perimeter and Area can help students to score well in the Class 6th board exam. 

Regular solving questions from the #Perimeter and Area Worksheet for Class 6 Worksheet PDF can help students to build a strong foundation for the chapter Perimeter and Area. Strong foundation of the chapter Perimeter and Area can help students to understand further chapters. 

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Area and perimeter of irregular rectangles

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Geometry worksheets: Area and perimeter of irregular rectangular shapes

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Arinjay Academy » Maths » Perimeter And Area Questions For Class 6

Perimeter And Area Questions For Class 6

Perimeter And Area Questions For Class 6, deals with various concepts which are as under:-

• Perimeter of Rectangle
• Perimeter of Square
• Perimeter of Triangle
• Perimeter of Equilateral Triangle
• Perimeter of regular pentagon
• Perimeter of regular octagon
• Perimeter of regular decagon
• Area of Rectangle
• Area of Square
• Circumference of a Circle
• Finding Diameter of a circle when  circumference is given 
• Finding Radius of a circle when circumference is given
• Finding Perimeter of Rectangle when Area & Breadth given
• Finding Perimeter of Rectangle when Area & Length given
• Find the dimensions of a rectangle
• Find the cost of fencing of a rectangular field
• Find the cost of carpeting the room

Perimeter And Area Questions For Class 6 – Perimeter of Rectangle

Perimeter of Rectangle is equal to twice of Sum of its length and breadth.

Perimeter of Rectangle Formula

Perimeter of Rectangle = 2 ( Length of Rectangle + Breadth of Rectangle )

Find the perimeter of a rectangle in which: length = 12 cm and  breadth = 5 cm

Explanation:

Given: Length = 12 cm Breadth = 5 cm Perimeter of Rectangle = 2 ( l + b ) units Perimeter of Rectangle = 2 ( 12 + 5 ) cm    (Here, Length = 12 cm , Breadth = 5 cm ) Perimeter of Rectangle = ( 2 x 17 ) cm Perimeter of Rectangle = 34 cm Hence, Perimeter of Rectangle is 34 cm

Perimeter And Area Questions For Class 6 – Perimeter of a Square

Perimeter of a Square is equal to four times of its side.

Perimeter of Square = 4 x Length of each side

Find the perimeter of a square, each of whose side is 14 cm ?

Square is a four sided polygon having all four sides equal in length.

Given: Side = 14 cm Perimeter of square = ( 4 x Length of each side ) units Perimeter of square = ( 4 x 14 ) cm Perimeter of square = 56 cm Hence, Perimeter of square is 56 cm

Perimeter And Area Questions For Class 6 – Perimeter of Triangle

Perimeter is the sum of all the sides of a closed figure. Triangle is a three-sided polygon. Perimeter of a triangle is equal to the sum of all the three sides of the triangle. Perimeter of Triangle = Sum of its 3 sides

Find the perimeter of a triangle of sides 11 cm, 5 cm and 8 cm ?

Explanation

Given: Ist side = 11 cm IInd side = 5 cm IIIrd side = 8 cm Perimeter of triangle = Sum of its sides Perimeter of triangle = ( Ist side + IInd side + IIIrd side ) cm Perimeter of triangle = ( 11 + 5 + 8 ) cm Perimeter of triangle = 24 cm Hence, Perimeter of triangle is 24 cm

Perimeter And Area Questions For Class 6 – Perimeter of an Equilateral Triangle

Perimeter is the sum of all the sides of a closed figure. An equilateral triangle is a triangle having all three sides equal in length. Perimeter of an equilateral triangle is equal to three times the length of a side of a triangle. Perimeter of an Equilateral Triangle = 3 x Length of each side

Find the perimeter of an equilateral triangle of side 9cm

An equilateral triangle is a triangle having all three sides equal in length. Length of each side of an equilateral triangle = 9 cm Perimeter of an equilateral triangle = ( 3 x Length of each side ) units Perimeter of an equilateral triangle = ( 3 x 9 ) cm Perimeter of an equilateral triangle = 27 cm Hence, Perimeter of an equilateral triangle is 27 cm

Perimeter And Area Questions For Class 6 – Perimeter of a Regular Pentagon

Perimeter is the sum of all the sides of a closed figure A regular pentagon is a five-sided polygon. All the five sides of regular pentagon are equal. Perimeter of a Regular Pentagon is equal to five times the length its side. Perimeter of Regular Pentagon = 5 x Length of each side

Find the perimeter of a regular pentagon of side 10cm

A regular pentagon is a five sided polygon. All the five sides of regular pentagon are equal. So, Length of each side of regular pentagon = 10cm Perimeter of a regular pentagon = ( 5 x Length of each side ) units = ( 5 x 10 ) cm = 50 cm Hence, Perimeter of a regular pentagon is 50 cm

Perimeter And Area Questions For Class 6 –  Perimeter of a Regular Octagon

Perimeter is the sum of all the sides of a closed figure A regular octagon is an eight-sided polygon. All eight sides of regular octagon are equal. Perimeter of a Regular Octagon is equal to eight times the length its side. Perimeter of Regular Octagon = 8 x Length of each side

Find the perimeter of a regular octagon of side 10cm

A regular octagon is an eight sided polygon. All eight sides of regular octagon are equal. So, Length of each side of regular octagon =10cm Perimeter of a regular octagon = ( 8 x Length of each side ) units = ( 8 x 10 ) cm = 80 cm Hence, Perimeter of a regular octagon is 80 cm

Perimeter And Area Questions For Class 6 – Perimeter of a Regular Decagon

Perimeter is the sum of all the sides of a closed figure A regular decagon is a ten-sided polygon whose all ten sides are equal in length. Perimeter of a Regular Decagon is equal to ten times the length its side. Perimeter of Regular Decagon = 10 x Length of each side

Find the perimeter of a regular decagon of side 4.5 cm

A regular decagon is a ten sided polygon that has all ten sides equal in length Length of a regular decagon =4.5 cm Perimeter of a regular decagon =(10 x Length of each side)units =(10 x 4.5) cm =45 cm Hence, Perimeter of a regular decagon is 45 cm

Perimeter And Area Questions For Class 6 – Area of Rectangle

Area of Rectangle is equal to the product of its length and breadth.

Area of Rectangle = Length x Breadth

Find the area of rectangle in which: length = 6 cm and breadth = 7 cm

Given, length = 6 cm breadth = 7 cm Area of rectangle = ( length x breadth ) = ( 6 x 7 ) cm² = 42 cm²

Hence, the area of rectangle is 42 cm²

Perimeter And Area Questions For Class 6 – Finding cost of fencing of a rectangular field

Find the cost of fencing of a rectangular field 20 m long and 35 m wide at ₹ 6 per metre.

Length of the field = 20 m Breadth of the field = 35 m Perimeter of the field = 2 ( l+b ) units = 2 ( 20 + 35 ) m = ( 2 x 55 ) m = 110 m

Cost of fencing per metre = ₹ 6

Total cost of fencing = ₹ ( 110 x 6 ) = ₹ 660

Perimeter And Area Questions For Class 6 –  Finding Length of rope fenced around Rectangular Field

Question 10

The length and the breadth of a rectangular field are 40 m and 60 m respectively. It is fenced with 2 round of rope. Find the length of the rope.

Length of the field = 40 m Breadth of the field = 60 m Perimeter of the field = 2 (l+b) units = 2 ( 40 + 60 ) m = ( 2 x 100 ) m = 200 m

Total length of rope = 2 x Perimeter of the field = ( 2 x 200 ) m = 400 m

Perimeter And Area Questions For Class 6 – Area of Square

Area of Square is equal to (length of its side x length of side).

Area of Square = ( side x side )  = (side)²

Question 11

Find the area of a square plot of side 2.5 cm

Sides of square = 2.5 cm

Area of square = ( side x side ) cm²

= ( 2.5 x 2.5 ) cm²

Hence, the area of square plot is 6.25 cm²

Perimeter And Area Questions For Class 6 – Finding Circumference of the circle when radius is given

Circumference of a circle is the measure of the length of the circle.

Circumference of a circle = 2πr

Question 12

Find the circumference of a circle of radius 49 cm?

The radius of given circle is r = 49 cm

Circumference of the circle = 2πr

= ( 2 x 22/7 x 49 ) cm

Hence, the circumference of the given circle is 308 cm

Perimeter And Area Questions For Class 6 – Finding Circumference of the circle when diameter is given

Question 13

Find the circumference of a circle, whose diameter is 56 cm?

The diameter of given circle = 56 cm

Circumference of circle = 2πr

= ( 2 x 22/7 x 28 ) cm

Hence, the circumference of the given circle is 176 cm

Perimeter And Area Questions For Class 6 – Radius of a Circle

Question 14

Find the radius of the circle whose circumference is 132 cm?

Let, the radius of the given circle be r cm

As we know that,

Circumference of the circle = 2πr cm

Circumference of a circle = 132cm

2πr = 132 (from above)

Hence, the radius of the circle = 21cm

Perimeter And Area Questions For Class 6 –  Finding Diameter of a circle when circumference is given

Question 15

Find the diameter of the circle whose circumference is 264 cm?

Circumference of a cicle = 264cm

2πr = 264 (from above)

Diameter of the circle = 2r

= (2 x 42)cm

Hence, the Diameter of the circle is 84 cm

Perimeter And Area Questions For Class 6 – Problem-based on circumference of a circle

Question 16

The diameter of a wheel of a car is 42 cm. Find the distance covered by the car during the time in which the wheel makes 1600 revolutions?

Radius of the wheel = 42/2 cm = 21 cm

Circumference of the wheel = 2πr

= 1.32 m ( As we know that, 1 m = 100 cm )

Distance covered by wheel in 1 revolution = Circumference of the wheel

Distance covered by wheel in 1 revolution = 1.32 m

Distance covered by wheel in 1600 revolutions = ( 1.32 x 1600 ) m

= 2.112 km ( As we know that, 1 m = 1000 km )

Hence, Distance covered by wheel in 1600 revolutions is 2.112 km

Perimeter And Area Questions For Class 6 – Finding Perimeter of Rectangle when Area & Breadth is given

Question 17

The area of a rectangle is 832 cm² and its breadth is 26 cm. Find the perimeter of the rectangle.

Given Area = 832 cm² breadth = 26 cm

Perimeter of the rectangle = 2 x ( l + b ) cm = 2 x ( 26 + 32 ) cm = ( 2 x 58 ) cm = 116 cm

Hence, the perimeter of the rectangle is 116 cm

Perimeter And Area Questions For Class 6 – Finding Perimeter of Rectangle when Area & Length are given

Question 18

The area of a rectangle is 85 cm² and its length is 5 cm . Find the perimeter of the rectangle.

Given Area = 85 cm² length = 5 cm

Perimeter of the rectangle = 2 x ( l + b ) cm = 2 x ( 5 + 17 ) cm = ( 2 x 22 ) cm = 44 cm

Hence, perimeter of the rectangle is 44 cm

Perimeter And Area Questions For Class 6 – Problem based on Perimeter of rectangle

Question 19

The length and the breadth of a rectangle are in the ratio 2 : 5 . If its perimeter is 28 m , find its dimensions.

Let, length and breadth be 2y m and 5y m

Since, perimeter of rectangle = 2 (l+b) units = 2 ( 2 y + 5 y ) m = ( 2 x 7 y ) m = 14ym

But, perimeter of rectangle = 28 m

Since, 14 y = 28 y = 28/14

So, length = ( 2 x 2 ) m = 4 m breadth = ( 5 x 2 ) m = 10 m

Perimeter And Area Questions For Class 6 – Problem based on cost of carpeting the room

Question 20

A room is 48 m long and 18 m broad. Find the cost of carpeting the room with a carpet of width  18 m at the rate of ₹ 50 per metre.

Length of the room = 48 m Breadth of the room = 18 m

Area of the floor of the room = ( 48 x 18 ) m² = 864 m²

Area of carpet required = 864 m²

Rate of carpeting = 50 per metre. Cost of carpeting = ₹ ( 48 x 50 ) = ₹ 2400

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Chickasaw national recreation area to open east perimeter drive in the platt historic district on monday may 6.

Contact: Public Affairs

SULPHUR, Okla. – On April 27, 2024, an EF-3 tornado touched down in Chickasaw National Recreation Area and caused significant damage to the park on its path towards downtown Sulphur. The main area impacted within the park was the western half of the Platt Historic District, including Flower Park and the maintenance yard. Heavy rainfall flooded creeks and lakes within the park as well, prompting a closure of the entire recreation area. National Park Service crews have been working diligently to safely open some sections of the park. Most of the Platt Historic District that is east of U.S. Route 177 will open to the public at 8 a.m. Monday morning. This opening includes the Southeast and Northeast Perimeter Drives, all trails east of the highway, the Travertine Nature Center and Little Niagara. However, Central Campground and Cold Springs Campgrounds will remain closed. “We are very pleased to be reopening the east side of Platt National Park Historic District, said Acting Superintendent Devon Bradley . “I commend the collective efforts of the National Park Service, the community of Sulphur, the Chickasaw Nation and all the people who have come together in our time of need. This is an important step on the road to healing our park and community.” All areas of the park west of Hwy. 177, including the western portion of the Platt National Park Historic District, all campgrounds, Veterans Lake, and Lake of the Arbuckles remain closed. Repairs are needed to many park buildings, roads, trails, bridges, and other infrastructure. All campground reservations and special use permits have currently been cancelled through May 13, and there may be further cancellations as conditions continue to be assessed. As you reenter the park, please stay in open areas and on established trails and picnic areas. There are still crews working west of Hwy. 177 with heavy equipment, and several types of active hazards still exist. For more information about Chickasaw National Recreation Area and for updates on park operations, visit  https://www.nps.gov/chic/planyourvisit/conditions.htm  or follow the park’s social media accounts, username ChickasawNPS, on  Facebook ,  X , and  Instagram . About the National Park Service More than 20,000 National Park Service employees care for America’s 429 National Parks and work with communities across the nation to help preserve local history and create close-to-home recreational opportunities. Learn more at www.nps.gov .

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