**Please check explanation and answers of Area and Perimeter Worksheets Grade 6 at the end of the questions.**

**Download Area and Perimeter Worksheets Grade 6**

**Q.1 Find the perimeter of a rectangle in which: length = 9 cm and breadth = 8 cm**

a) 17 cm

b) 72 cm

c) 32 cm

d) 34 cm

**Q.2 Find the perimeter of a square, each of whose side is 12 cm**

a) 36 cm

b) 24 cm

c) 50 cm

d) 48 cm

**Q.3 Find the perimeter of a triangle of sides 11 cm , 4 cm and 5 cm**

a) 20 cm

b) 22 cm

c) 19 cm

d) 21 cm

**Q.4 Find the perimeter of an equilateral triangle of side 9cm**

a) 26 cm

b) 29 cm

c) 27 cm

d) 29 cm

**Q.5 Find the perimeter of a regular pentagon of side 3cm**

a) 12 cm

b) 15 cm

c) 18 cm

d) 21 cm

**Q.6 Find the perimeter of a regular decagon of side 3.6cm**

a) 14.4 cm

b) 36 cm

c) 21.6 cm

d) 25.2 cm

**Q.7 Find the perimeter of a regular octagon of side 7cm**

a) 56 cm

b) 28 cm

c) 42 cm

d) 49 cm

**Q.8 Find the area of rectangle in which: length = 6 cm and breadth = 10 cm**

a) 60

b) 32

c) 16

d) 76

**Q.9 Find the area of a square plot of side 4 cm**

a) 20

b) 16

c) 12

d) 14

**Q.10 Find the circumference of a circle of radius 28 cm**

a) 194 cm

b) 166 cm

c) 190 cm

d) 176 cm

**Q.11 Find the circumference of a circle, whose diameter is 14 cm**

a) 47 cm

b) 42 cm

c) 44 cm

d) 48 cm

**Q.12 Find the radius of the circle whose circumference is 440cm**

a) 70 cm

b) 72 cm

c) 68 cm

d) 73 cm

**Q.13 Find the diameter of the circle whose circumference is 44cm**

a) 7 cm

b) 5 cm

c) 14 cm

d) 12 cm

**Q.14 The length and the breadth of a rectangular field are 80 m and 60 m respectively. It is fenced with 3 round of rope. Find the length of the rope.**

a) 840 m

b) 280 m

c) 560 m

d) 1120 m

**Q.15 The diameter of a wheel of a car is 140 cm . Find the distance covered by the car during the time in which the wheel makes 1000 revolutions .**

a) 4.43 km

b) 4.399 km

c) 5.4 km

d) 4.4 km

**Q.16 A room is 125 m long and 10 m broad . Find the cost of carpeting the room with a carpet of width 5 m at the rate of ₹ 20 per metre.**

a) ₹ 4917

b) ₹ 5000

c) ₹ 5083

d) ₹ 4750

**Q.17 The length and the breadth of a rectangle are in the ratio 3 : 5 . If its perimeter is 32 m , find its dimensions.**

a) Length = 10 m , breadth = 6 m

b) Length = 12 m , breadth = 8 m

c) Length = 6 m , breadth = 10 m

d) Length = 8 m , breadth = 12 m

**Q.18 Find the cost of fencing of a rectangular field 65 m long and 55 m wide at ₹ 10 per metre.**

a) ₹ 615

b) ₹ 2400

c) ₹ 2900

d) ₹ 3400

**Q.19 The area of a rectangle is 600 and its breadth is 30 cm . Find the perimeter of the rectangle.**

a) 113 cm

b) 100 cm

c) 117 cm

d) 87 cm

**Q.20 The area of a rectangle is 108 and its length is 12 cm . Find the perimeter of the rectangle.**

a) 55 cm

b) 42 cm

c) 59 cm

d) 29 cm

### Area and Perimeter Worksheets Grade 6 Explanations

**Area and Perimeter Worksheets Grade 6 – Explanation 1-**

Rectangle is a four sided polygon having equal opposite sides

Given:

Length = 9 cm

Breadth = 8 cm

Perimeter of rectangle = 2 ( l + b ) units

= 2 ( 9 + 8 ) cm (Here, Length = 9 cm , Breadth = 8 cm )

= ( 2 x 17 ) cm

= 34 cm

Hence, Perimeter of rectangle is 34 cm

**Correct Answer – d) 34 cm**

**Area and Perimeter Worksheets Grade 6 – Explanation 2-**

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

Given:

Side = 12 cm

Perimeter of square = ( 4 x Length of each side ) units

= ( 4 x 12 ) cm

= 48 cm

Hence, Perimeter of square is 48 cm

**Correct Answer – d) 48 cm**

**Area and Perimeter Worksheets Grade 6 – Explanation 3-**

Triangle is a three sided polygon.

Given:

Ist side = 11 cm

IInd side = 4 cm

IIIrd side = 5 cm

Perimeter of triangle = Sum of its sides

= ( Ist side + IInd side + IIIrd side ) cm

= ( 11 + 4 + 5 ) cm

= 20 cm

Hence, Perimeter of triangle is 20 cm

**Correct Answer – a) 20 cm**

**Area and Perimeter Worksheets Grade 6 – Explanation 4-**

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

= ( 3 x 9 ) cm

= 27 cm

Hence, Perimeter of an equilateral triangle is 27 cm

**Correct Answer – c) 27 cm**

**Area and Perimeter Worksheets Grade 6 – Explanation 5-**

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 = 3cm

Perimeter of a regular pentagon = ( 5 x Length of each side ) units

= ( 5 x 3 ) cm

= 15 cm

Hence, Perimeter of a regular pentagon is 15 cm

**Correct Answer – b) 15 cm**

**Area and Perimeter Worksheets Grade 6 – Explanation 6-**

A regular decagon is a ten sided polygon that has all ten sides equal in length

Length of a regular decagon =3.6

Perimeter of a regular decagon =(10xLength of each side)units

=(10×3.6)cm

=36cm

Hence, Perimeter of a regular decagon is 36cm

**Correct Answer – b) 36 cm**

**Area and Perimeter Worksheets Grade 6 – Explanation 7-**

A regular octagon is an eight sided polygon.

All eight sides of regular octagon are equal.

So, Length of each side of regular octagon =7cm

Perimeter of a regular octagon = ( 8 x Length of each side ) units

= ( 8 x 7 ) cm

= 56 cm

Hence, Perimeter of a regular octagon is 56 cm

**Correct Answer – a) 56 cm**

**Area and Perimeter Worksheets Grade 6 – Explanation 8-**

Given,

length = 6 cm

breadth = 10 cm

Area of rectangle = ( length x breadth )

= ( 6 x 10 )

= 60

Hence, the area of rectangle is 60

**Correct Answer – a) 60 **

**Area and Perimeter Worksheets Grade 6 – Explanation 9-**

Sides of square = 4cm

Area of square = ( side x side )

= ( 4 x 4 )

= 16

Hence, the area of square plot is 16

**Correct Answer – b) 16 **

**Area and Perimeter Worksheets Grade 6 – Explanation 10-**

The radius of given circle is r = 28 cm

Circumference of the circle = 2∏r

= ( 2 x x 28 ) cm

= 176 cm

Hence, the circumference of the given circle is 176 cm

**Correct Answer – d) 176 cm**

**Area and Perimeter Worksheets Grade 6 – Explanation 11-**

The diameter of given circle = 14 cm

Then, radius = = cm = 7 cm

Circumference of circle = 2∏r

= ( 2 x x 7 ) cm

= 44 cm

Hence, the circumference of the given circle is 44 cm

**Correct Answer – c) 44 cm**

**Area and Perimeter Worksheets Grade 6 – Explanation 12-**

Let, the radius of the given circle be r cm

As we know that,

Circumference of the circle = 2∏r cm

Given,

Circumference of a circle = 440cm

2∏r = 440 (from above)

r =

=

= 70cm

Hence, the radius of the circle = 70cm

**Correct Answer – a) 70 cm**

**Area and Perimeter Worksheets Grade 6 – Explanation 13-**

Let, the radius of the given circle be r cm

As we know that,

Circumference of the circle = 2∏r cm

Given,

Circumference of a cicle = 44cm

Therefore,

2∏r = 44 (from above)

r =

=

= 7cm

Diameter of the circle = 2r

= (2 x 7)cm

= 14cm

Hence, the Diameter of the circle is 14 cm

**Correct Answer – c) 14 cm**

**Area and Perimeter Worksheets Grade 6 – Explanation 14-**

Length of the field = 80 m

Breadth of the field = 60 m

Perimeter of the field = 2 (l+b) units

= 2 ( 80 + 60 ) m

= ( 2 x 140 ) m

= 280 m

Total length of rope = 3 x Perimeter of the field

= ( 3 x 280 ) m

= 840 m

**Correct Answer – a) 840 m**

**Area and Perimeter Worksheets Grade 6 – Explanation 15-**

Radius of the wheel = cm = 70 cm

Circumference of the wheel = 2∏r

= ( 2 x x 70 ) cm

= 440 cm

= 4.4 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 = 4.4 m

Distance covered by wheel in 1000 revolutions = ( 4.4 x 1000 ) m

= 4400 m

= 4.4 km ( As we know that, 1 m = 1000 km )

Hence, Distance covered by wheel in 1000 revolutions is 4.4 km

**Correct Answer – d) 4.4 km**

**Area and Perimeter Worksheets Grade 6 – Explanation 16-**

Length of the room = 125 m

Breadth of the room = 10 m

Area of the floor of the room = ( 125 x 10 )

= 1250

Area of carpet required = 1250

Length of the carpet = = = = 250 m

Rate of carpeting = 20 per metre.

Cost of carpeting = ₹ ( 250 x 20 ) = ₹ 5000

**Correct Answer – b) ₹ 5000 **

**Area and Perimeter Worksheets Grade 6 – Explanation 17-**

Let, length and breadth be 3y m and 5y m

Since, perimeter of rectangle = 2 (l+b) units

= 2 ( 3 y + 5 y ) m

= ( 2 x 8 y ) m

= 16ym

But, perimeter of rectangle = 32 m

Since, 16 y = 32

y =

y = 2

So, length = ( 3 x 2 ) m = 6 m

breadth = ( 5 x 2 ) m = 10 m

**Correct Answer – c) Length = 6 m , breadth = 10 m**

**Area and Perimeter Worksheets Grade 6 – Explanation 18-**

Length of the field = 65 m

Breadth of the field = 55 m

Perimeter of the field = 2 ( l+b ) units

= 2 ( 65 + 55 ) m

= ( 2 x 120 ) m

= 240 m

Cost of fencing per metre = ₹ 10

Total cost of fencing = ₹ ( 240 x 10 )

= ₹ 2400

**Correct Answer – b) ₹ 2400 **

**Area and Perimeter Worksheets Grade 6 – Explanation 19-**

Given

Area = 600

breadth = 30 cm

Length of the rectangle = = = = 20 cm

Perimeter of the rectangle = 2 x ( l + b ) cm

= 2 x ( 30 + 20 ) cm

= ( 2 x 50 ) cm

= 100 cm

Hence, the perimeter of the rectangle is 100 cm

**Correct Answer – b) 100 cm**

**Area and Perimeter Worksheets Grade 6 – Explanation 20-**

Given

Area = 108

length = 12 cm

Breadth of the rectangle = = = = 9 cm

Perimeter of the rectangle = 2 x ( l + b ) cm

= 2 x ( 12 + 9 ) cm

= ( 2 x 21 ) cm

= 42 cm

Hence, perimeter of the rectangle is 42 cm

**Correct Answer – b) 42 cm**

### Free Math Worksheets for Class 6

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