Ncert solutions mathematics class 6 Solutions for Chapter 10 mensuration

Exercises in Chapter 10 mensuration Grade 6

Exercise 10.1

Exercise 10.2

Exercise 10.3

Questions in Exercise 10.1

Q1) Find the perimeter of each of the following figures:

(a)

(b)

(c)

(d)

(e)

(f)

Find the perimeter of each of the following figures:

The lid of a rectangular box of sides 40 cm by 10 cm is sealed all around with tape. What is the length of the tape required?

Q2) 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?

Q3) A table-top measures 2 m 25 cm by 1 m 50 cm. What is the perimeter of the table-top?

A table top measures 2 m 25 cm by 1 m 50 cm. What is the perimeter of the table top?

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

Q4) What is the length of the wooden strip required to frame a photograph of length and breadth 32 cm and 21 cm respectively?

Q5) 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?

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?

Q6) 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.

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

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

Q7) Find the perimeter of a triangle with sides measuring 10 cm, 14 cm, and 15 cm.

Q8) Find the perimeter of a regular hexagon with each side measuring 8 cm.

Q9) Find the side of the square whose perimeter is 20 m.

Find the side of the square whose perimeter is 20 m.

Q10) The perimeter of a regular pentagon is 100 cm. How long is its each side?

A piece of strings 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?

Q11) 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

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

Q12) Two sides of a triangle are 12 cm and 14 cm. The perimeter of the triangle is 36 cm. What is the third side?

Q13) Find the cost of fencing a square park of side 250 m at the rate of 20 per meter.

Find the cost of fencing a square park of side 250 m at the rate of ₹ 20 per metre.

Q14) Find the cost of fencing a rectangular park of length 175 m and breadth 125 m at the rate of Rs. 12 per meter.

Find the cost of fencing a rectangular park of length 175 cm and breadth 125 m at the rate of ₹ 12 per metre.

Q15) Sweety runs around a square park of side 75 m. Bulbul runs around a rectangular park with a length of 60 m and breadth 45 m. Who covers less distance?

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?

What is the perimeter of each of the following figures? What do you infer from the the answers?

Q16) What is the perimeter of each of the following figures? What do you infer from the answer?

(a)

(b)

(c)

(d)

Avneet buys 9 square paving slabs, each with a side of 1 / 2 m. 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)]?

(d) Avneet wonders if there is a way of getting an even greater perimeter. Can you find a way of doing this? (The paving slabs must meet along complete edges i.e they cannot be broken.)

Q17) Avneet buys 9 square paving slabs, each with a side $\frac{1}{2}$ m. He lays them in the form of a square

(a)What is the perimeter of his arrangement?

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

(c)Which has a greater perimeter?

(d)Avneet wonders, if there is a way of getting an even greater perimeter. Can you find a way of doing this? (The paving slabs must meet along complete edges, i.e., they cannot be broken.)

Questions in Exercise 10.2

Q1) Find the areas of the following figures by counting squares:

Find the areas of the following figures by counting square:

Questions in Exercise 10.3

Q1) Find the areas of the rectangles whose sides are:

(a) 3 cm and 4 cm

(b) 12 m and 21 m

(d) 2 m and 70 cm

Find the area of the rectangles whose sides are:

(a) 3 cm and 4 cm

(b) 12 m and 21 m

(d) 2 m and 70 cm

Q2) Find the areas of the squares whose sides are:

(a) 10 cm

(b) 14 cm

Find the areas of the squares whose sides are:

(a) 10 cm

(b) 14 cm

Q3) The length and the breadth of three rectangles are as given below:

(a) 9 m and 6 m

(b) 17 m and 3 m

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

Q4) The area of a rectangle garden 50 m long is 300 m.sq, find the width of the garden.

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

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

Q5) What is the cost of tilling a rectangular plot of land 500 m long and 200 m wide at the rate of Rs. 8 per hundred sq. m?

Q6) A table-top measures 2 m by 1 m 50 cm. What is its area in square meters?

A table top measures 2 m by 1 m 50 cm. What is its area in square metres?

A room is 4 m long and 3 m 50 cm wide. Howe many square metres of carpet is needed to cover the floor of the room?

Q7) A room us 4 m long and 3 m 50 cm wide. How many square meters of carpet are needed to cover the floor of the room?

Q8) 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.

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.

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?

Q9) 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?

By splitting the following figures into rectangles, find their areas (The measures are given in centimetres).

Q10) By splitting the following figures into rectangles, find their areas. (The measures are given in centimeters)

(a)

(b)

Q11) Split the following shapes into rectangles and find their areas. (The measures are given in centimeters)

(a)

(b)

(c)

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

Q12) 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

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