**Ncert Class 6 Mathematics Solutions Chapter 10 Mensuration**

Welcome to NCTB Solutions. Here with this post we are going to help 6th class students for the Solutions of NCERT Class 6 Mathematics Book, Chapter 10, Mensuration. Here students can easily find step by step solutions of all the problems for Mensuration, Exercise 10.1, 10.2 and 10.3 Also here our mathematics teacher’s are solved all the problems with easily understandable methods with proper guidance so that all the students can understand easily. Here in this post students will get chapter 10 solutions. Here all the solutions are based on NCERT latest syllabus.

**Mensuration Exercise 10.1 Solution : **

**(2) The lid of a rectangular box of sides 40 cm by 10 cm is sealed all round with tape. What is the length of the tape required?**

**Solution : **

The length of the tape required = 2 x (Length + breadth)

The length of the tape required

= 2 × ( 40 + 10 )

= 2 × 50 = 100 cm

Thus, the length of the tape required is 100 cm.

**(3) A table-top measures 2 m 25 cm by 1 m 50 cm. What is the perimeter of the table-top?**

**Solution :**

As we know,

Perimeter = 2 x (Length + breadth)

The perimeter of the table-top,

= 2 × (2 m 25 cm + 1 m 50 cm)

= 2 × 3. 75

= 7.5 m

Hence, the perimeter of the table-top will be 7.5 m

**(4) What is the length of the wooden strip required to frame a photograph of length and breadth 32 cm and 21 cm respectively?**

**Solution : **

Given, Length = 32 cm

and breadth 21 cm

The length of the wooden strip required to frame a photograph,

= 2 × (Length + breadth)

= 2 × (32 + 21)

= 106 cm

Therefore, length of the wooden strip required to frame a photograph is 106 cm.

**(5) A rectangular piece of land measures 0.7 km by 0.5 km. Each side is to be fenced with 4 rows of wires. What is the length of the wire needed?**

**Solution : **

A rectangular piece of land measures = 0.7 km by 0.5 km.

Length of the wire needed,

= 2 × (Length + breadth)

= 2 × (0.7 + 0.5)

= 2.4 km

Each side is to be fenced with 4 rows of wires.

= 2.4 km × 4

= 9.6 km

Therefore, the needed length of the wire will be 9.6 km.

**(6) Find the perimeter of each of the following shapes :**

**(a) A triangle of sides 3 cm, 4 cm and 5 cm.**

**(b) An equilateral triangle of side 9 cm.**

**(c) An isosceles triangle with equal sides 8 cm each and third side 6 cm.**

**Solution : **

**(i) Perimeter = s1 + s2 + s3**

Perimeter,

= 3 + 4 + 5

= 12 cm

Hence, perimeter of a triangle of sides 3 cm, 4 cm and 5 cm is 12 cm.

**(ii) Perimeter = 3 × side**

Perimeter

= 3 × 9

= 27 cm.

Hence, perimeter of an equilateral triangle of side 9 cm

**(iii) Perimeter = 2 × equal side + 3rd side**

Perimeter,

= 2 × 8 + 6

= 16 + 6

= 22 cm.

Hence, perimeter of an isosceles triangle with equal sides 8 cm each and third side of 6 cm is 22 cm.

**(7) Find the perimeter of a triangle with sides measuring 10 cm, 14 cm and 15 cm.**

**Solution : **

Perimeter of a triangle = Addition of all sides

= 10 cm + 14 cm + 15 cm

= 39 cm

Thus, the perimeter of a triangle will be 39 cm.

**(8) Find the perimeter of a regular hexagon with each side measuring 8 m.**

**Solution : **

Given, Side of regular hexagon = 8 m

**∴** Perimeter,

= (6 × 8)

= 48 m

So, the perimeter of a regular hexagon is 48 m.

**(9) Find the side of the square whose perimeter is 20 m.**

**Solution : **

Perimeter of square = 4 × sides.

Perimeter of square

= 4 × 20

= 80 m

Thus, the side of the square will be 80 m.

**(10) The perimeter of a regular pentagon is 100 cm. How long is its each side?**

**Solution : **

We know, Regular pentagon has 5 sides.

The perimeter of a regular pentagon is 100 cm.

**∴** Each side,

= 100/5

= 20 cm

**(11) A piece of string is 30 cm long. What will be the length of each side if the string is used to form :**

**(a) a square?**

**(b) an equilateral triangle?**

**(c) a regular hexagon?**

**Solution : **

**(a) A square?**

String is 30 cm long

Side = 30/4

= 7.5 cm

**(b) An equilateral triangle?**

String is 30 cm long

Side = 30/3

= 10 cm

**(c) A regular hexagon?**

String is 30 cm long

Side = 30/6

= 5 cm

**(12) Two sides of a triangle are 12 cm and 14 cm. The perimeter of the triangle is 36 cm. What is its third side?**

**Solution : **

Let sides of triangle is s1, s2 and s3.

Given, Two sides of a triangle are 12 cm and 14 cm. The perimeter of the triangle is 36 cm.

So, s1 = 12 cm, s2 = 14 cm and perimeter of triangle is 36 cm

To find tired side i.e. s3.

Thus, perimeter

= s1 + s2 + s3,

36 = 12 + 14 + s3

36 = 26 + s3

s3 = 36 – 26

= 10 cm

Therefore, third side of triangle is 10 cm.

**(13) Find the cost of fencing a square park of side 250 m at the rate of Rs 20 per metre.**

**Solution : **

Square Park of side 250 m

The cost of fencing a square park = 4 × side

4 × 250 = 1000 m.

Rate of 20 per metre.

1000 × 20 = Rs.20, 000

The cost of fencing a square park of side 250 m is Rs. 20,000

**(14) Find the cost of fencing a rectangular park of length 175 m and breadth 125 m at the rate of Rs 12 per metre.**

**Solution : **

**∴** Perimeter,

= 2 (175 + 125)

= 2 × 300

= 600 m

**∴** Cost,

= 600 × 12

= 7200 rupees

Thus, the cost of fencing a rectangular will be 7200 rupees.

**(15) Sweety runs around a square park of side 75 m. Bulbul runs around a rectangular park with length 60 m and breadth 45 m. Who covers less distance?**

**Solution : **

Perimeter of Square park,

= 4 × 75

= 300 m

Perimeter of rectangular park,

= 2 × (Length + Breadth)

= 2 × ( 60 + 45)

= 210 m

Therefore, Bulbul covers less distance.

**(16) What is the perimeter of each of the following figures? What do you infer from the answers?**

**Solution : **

**(i)** Perimeter = addition of all sides.

So, 25 + 25 + 25 + 25

= 100 cm

**(ii)** 20 + 20 + 30 + 30

= 100 cm

The perimeter of the following figure is 100 cm.

**(iii)** 10 + 10 + 40 + 40

= 100 cm

The perimeter of the following figure is 100 cm.

**(iv)** 30 + 30 + 40

= 100 cm

The perimeter of the following figure is 100 cm.

**(17) Avneet buys 9 square paving slabs, each with a side of 1m. He lays them in the form of a square**

**(a) What is the perimeter of his arrangement [Fig (i)]?**

**(b) Shari does not like his arrangement. She gets him to lay them out like a cross. What is the perimeter of her arrangement [Fig (ii)]?**

**(c) Which has greater perimeter?**

**(d) Avneet wonders if there is a way of getting an even greater perimeter. Can you find a way of doing this?**

**Solution : **

**(a)** Perimeter

= 1/2 × 3 × 4

= 6 m

**(b)** 1/2 × 5 × 4

= 10 m

**(c)** The fraction of cross has greater perimeter.

**(d)** No there is no such arrangement.

**Mensuration Exercise 10.3 Solution : **

**(1) Find the areas of the rectangles whose sides are :**

**(a) 3 cm and 4 cm**

**(b) 12 m and 21 m**

**(c) 2 km and 3 km**

**(d) 2 m and 70 cm**

**Solution : **

**(a)** We know,

Area of the rectangle = Length x Breadth

So, 3 cm x 4 cm

= 12 cm

Thus, Area of the rectangle will be 12 sq. cm.

**(b)** 12 m and 21 m

= 12 x 21

= 252

**∴** Area of the rectangle will be 252 sq. m.

**(c)** 2 km and 3 km

= 2 x 3

= 6

**∴** Area of the rectangle = 6 sq. km.

**(d)** 2 m and 70 cm

= 2 m x 0.7 m

= 1.40

**∴** Area of the rectangle will be 1.40 sq. m.

**(2) Find the areas of the squares whose sides are :**

**(a) 10 cm**

**(b) 14 cm**

**(c) 5 m**

**Solution : **

**(a)** As we know,

Area of the square = side x side

= 10 cm x 10 cm

= 100

**∴** Area of the square is 100 sq. cm.

**(b)** 14 cm

= 14 cm x 14 cm

= 196

**∴** Area of the square is 196 sq. cm.

**(c)** 5 m

= 5 m x 5 m

= 25

**∴** Area of the square is 25 sq. m.

**(3) The length and breadth of three rectangles are as given below :**

**(a) 9 m and 6 m**

**(b) 17 m and 3 m**

**(c) 4 m and 14 m**

**Which one has the largest area and which one has the smallest?**

**Solution : **

**(a)** We know,

Area of the rectangle = Length x Breadth

= 9 x 6

= 54

Area of the rectangle = 54 sq. m

**(b)** 17 m and 3 m

= 17 x 3

= 51

Area of the rectangle = 51 sq. m

**(4) The area of a rectangular garden 50 m long is 300 sq m. Find the width of the garden.**

**Solution : **

Area of the rectangle = Length x Breadth

300 sq. m = 50 x ?

Breadth = 300/50

= 6 m

Therefore, Width of the garden is 6 m.

**(5) What is the cost of tiling a rectangular plot of land 500 m long and 200 m wide at the rate of Rs 8 per hundred sq m.?**

**Solution : **

Area of the rectangle = Length x Breadth

500 m long x 200 m = 1, 00,000 sq. m.

Rate of 8 per hundred sq. m.

= 1, 00,000/100

= 1000 sq.

= 8 x 1000

= Rs.8000

Hence, cost of tiling a rectangular plot of land 500 m long and 200 m wide is Rs.8000.

**(6) A table-top measures 2 m by 1 m 50 cm. What is its area in square metres?**

**Solution : **

The perimeter of the table-top

= 2 x (Length + breadth)

The perimeter of the table-top

= 2 x (2 m 25 cm + 1 m 50 cm. )

= 2 x 3. 75

= 7.5 m

**∴** The perimeter of the table-top is 7.5 m

**(7) A room is 4 m long and 3 m 50 cm wide. How many square metres of carpet is needed to cover the floor of the room?**

**Solution : **

A room is 4 m long and 3 m 50 cm wide.

Area of the rectangle = Length x Breadth

= 4 m x 3 m 50 cm

= 14 sq. m

**∴** Carpet is needed to cover the floor of the room is 14 sq. m

**(8) A floor is 5 m long and 4 m wide. A square carpet of sides 3 m is laid on the floor. Find the area of the floor that is not carpeted.**

**Solution : **

Area of the rectangle floor = Length x Breadth

= 5 x 4

= 20 sq. m

A square carpet of sides 3 m.

Area of A square carpet

= Side x side

= 3 x 3

= 9 sq. m

Therefore, area of the floor that is not carpeted

= 20 sq. m – 9 sq. m

= 11 sq.m.

**(9) Five square flower beds each of sides 1 m are dug on a piece of land 5 m long and 4 m wide. What is the area of the remaining part of the land?**

**Solution : **

Area of A square flower beds = Side x side

= 1 x 1

= 1 sq. m

Five square flower beds

= 5 x 1

= 5 sq.m

Land 5 m long and 4 m wide

Area of the rectangle and = Length x Breadth

= 5 x 4

= 20 sq. m.

Area of the remaining part of the land

= 20 sq. m. – 5 sq.m

= 15 sq.m

**(11) Split the following shapes into rectangles and find their areas. (The measures are given in centimetres)**

**Solution** :

Figure – **(a)**

= (10 × 2) + 910 × 2)

= 40 square unit

Figure – **(b)**

= (7 × 7) × 5

= 245 square units

Figure – **(c)**

= (4 × 1) + (5 × 1)

= 9 square units

**(12) How many tiles whose length and breadth are 12 cm and 5 cm respectively will be needed to fit in a rectangular region whose length and breadth are respectively :**

**(a) 100 cm and 144 cm**

**(b) 70 cm and 36 cm.**

**Solution : **

**(a) Tiles whose length and breadth are 12 cm and 5 cm respectively**

Area of tiles

= 12 x 5

= 60 sq. m

Area of rectangular region

= 100 x 144

= 14,400 sq. m

Tiles needed,

= 14,400/60 sq. m

= 240

Thus, 240 tiles will be required.

**(b) Tiles whose length and breadth are 12 cm and 5 cm respectively.**

Area of tiles,

= 12 x 5

= 60 sq. m

Area of rectangular region,

= 70 x 36

= 2520 sq. m

Tiles needed,

= 2520/60 sq. m

= 42

Therefore, 42 Tiles will be required.

**Next Chapter Solution : **

👉 Chapter 11 👈