**Mensuration**

**Question 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)** Length of the rectangle = 4 cm

Breadth of the rectangle = 3 cm

Area = Length x Breadth

= 4 cm x 3 cm

= 12 sq. cm

**(b)** Length of the rectangle = 21 m

Breadth of the rectangle = 12 m

Area = Length x Breadth

= 21 m xl2 m

= 252 sq. m.

**(c)** Length of the rectangle = 3 km

Breadth of the rectangle =2 km

Area = Length x Breadth

= 3 km x 2km

= 6 sq. km

**(d)** Length of the rectangle =2m = 2 x l00= 200 cm

Breadth of the rectangle = 70 cm

Area = Length x Breadth

= 200 cm x 70 cm

= 14000 sq. cm

**Question 2.Find the areas of the squares whose sides are:**

**(a)**10 cm

**(b)**14 cm

**(c)**5 m

**Solution:****(a)** Side of the square = 10 cm

Area = (side)^{2}

= (10)^{2} sq. cm

= 100 sq. cm

**(b)** Side of the square = 14 cm

Area = (side)^{2}

= (14)^{2} sq. cm

= 196 sq. cm

**(c)** Side of the square = 5 m

Area = (side)^{2}

= (5)^{2} sq. m = 25sq. m

**Question 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:**

In rectangle (a), Area = (9 x 6) sq. m

= 54 sq. m

In rectangle (b), Area =(3 x 17) sq. m = 51 sq. m

In rectangle (c), Area = (4 x 14) sq. m = 56 sq. m

Clearly, 56 > 54 > 51 i.e., 56 is the largest number and 51 is the smallest number.

∴ The rectangle (c) has the largest area and the rectangle (a) has the smallest area.

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

**Solution:**

We use the formula A = l x b, where l is the length and b is the breadth of the rectangle in metre and its area in m2.

Here, A = 300 m^{2}, and l = 50 m

Therefore, 300 =50 x b [ ∵ A = l x b]

or

Hence the breadth (width) of the rectangle is 6 m.

**Question 5.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?**

**Solution:**

Area of rectangular piece of land = 500 x 200 sq. m

= 100000 sq. m

Cost of tiling the land at the rate of ₹ 8 per hundred sq. m

= ₹ = ₹ 8000

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

**Solution:**

Length of table’s top = 2 m

Breadth of table’s top = 1 m 50 cm = 1.50 m

∴ Area = Length x Breadth

= (2 x 1.50) sq m = 3 sq m

**Question 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:**

Length of the room = 4 m

Breadth of the room = 3 m 50 cm = 3.50 m

Carpet needed to cover the floor of the room

= Area of the floor of the room

= Length x Breadth

= (4 x 3.50) sq. m = 14 sq. m

**Question 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 floor of the room = (5 x 4) sq. m

= 20 sq. m

Area of the carpet = (3 x 3) sq. m = 9 sq. m

Area of the floor not carpeted = (20 – 9) sq. m

= 11 sq. m

**Question 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 the piece of land =(5 x 4) sq. m

= 20 sq. m

Area of square flower bed =(1 x 1) sq. m

= 1 sq. m

Area of 5 such flower beds =(5 x 1) sq. m

= 5 sq. m

∴ Area of the remaining part of land

= (20 – 5) sq. m = 15 sq. m

**Question 10.By splitting the following figures into rectangles, find their areas (The measures are given in centimetres).**

**Solution:**

**(a)**Let the figure may be divided into rectangles marked as A, B, C etc. Area of rectangle (A) = (3 x 3) sq. cm = 9 sq. cm

Area of rectangle (B) = (1 x 2) sq. cm = 2 sq. cm

Area of rectangle (C) = (3 x 3) sq. cm = 9 sq. cm

Area of rectangle (D) = (4 x 2) sq. cm = 8 sq. cm

∴ The total area of the figure = (9 + 2 + 9 + 8) sq. cm = 28 sq. cm

**(b)**Let the figure may be divided into rectangle marked as shown.

Area of rectangle (A) = (2 x 1) sq cm = 2 sq cm

Area of rectangle (B) = (5 x 1) sq cm = 5 sq cm

Area of rectangle (C) = (2 x 1) sq cm = 2 sq cm

∴ Total area of the figure = (2 + 5 + 2) sq cm = 9 sq cm

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

**Solution:**

**(a)**Splitting the given shape into rectangles as marked A and B.

Area of the rectangle (A) = (10 x 2) sq cm

= 20 sq cm

Area of the rectangle (B) = (10 x 2) sq cm

= 20 sq cm

∴ Total area of given shape = (20 +20) sq cm

= 40 sq cm

**(b)**Splitting the given shape into five squares each of side 7 cm.

Area of the given shape

= 5 x Area of one square of side 7 cm = 5 x (7 x 7) sq. cm

= (5 x 49)sq cm 7

= 245 sq cm

**(c)**Splitting the given shape into two rectangles named A and B. Area of rectangle (A) = (5 x 1) sq cm = 5 sq cm

Area of rectangle (B) = (4 x 1) sq cm = 4 sq cm

∴ Total area of given shape = (5 + 4) sq cm = 9 sq cm

**Question 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)** Area of the rectangular region

= (100 x 144) sq cm

= 14400 sq cm

Area of one tile = (5 x 12) sq cm

= 60 sq cm**(b)** Area of the rectangular region

= (70 x 36) sq cm

= 2520 sq cm