## Chapter 11 Mensuration Exercise 11.1

Question 1: A square and a rectangular field with measurements as given in the figure have the same perimeter. Which field has a larger area?

Answer:

Given

Side of square = 60 m

Rectangle length = 80 m

Square and rectangle have same perimeter.

To find

Which field has a larger area?

Formula

Perimeter of square = 4 × s

Perimeter of rectangle = 2(l + b)

Area of square = s²

Area of rectangle = l × b

Working

= 4 × s = 2(l + b)

= 4 × 60 = 2(80 + b)

= 240 = 160 + 2b

= 2b = 240 - 160

= 2b = 80

= b = 40 m

Area of square = ?

= s × s

= 60 × 60

= 3600 m²

Area of rectangle = ?

= l × b

= 80 × 40

= 3200 m²

Comparing

3600 m² > 3200 m²

Therefore, square has a larger area.

Question 2: Mrs. Kaushik has a square plot with the measurement as shown in the figure. She wants to construct a house in the middle of the plot. A garden is developed around the house. Find the total cost of developing a garden around the house at the rate of Rs 55 per m².

Answer:

Given

Length of side of square plot = 25 m

Length of house = 20 m

Breadth of house = 15 m

Cost of developing garden around the house per m² = ₹55

To find

The total cost of developing a garden around the house.

Formula

Area of square = s × s

Area of rectangle = l × b

Working

Area of square plot = ?

= 25 × 25

= 625 m²

Area of house = ?

= 20 × 15

= 300 m²

Area of garden = Area of square plot - Area of house

= 625 - 300

= 325 m²

Cost of developing garden around the house = ?

= 325 × 55

= ₹17875

Therefore, the cost of developing garden around the house is ₹17875.

Question 3: The shape of a garden is rectangular in the middle and semi circular at the ends as shown in the diagram. Find the area and the perimeter of this garden [Length of rectangle is 20 - (3.5 + 3.5) metres].

Answer:

Given

Shape of garden is in the form of rectangle in middle and semi circle at the ends.

Rectangle

length = 13 m

breadth = 7 m

Radius of circle = 3.5 m

To find

The area and the perimeter of this garden

Formula

Perimeter of rectangle = 2(l + b)

Perimeter of circle = 2πr

Area of rectangle = l × b

Area of circle = πr²

Working

Area of park = ?

= Area of semi circle + Area of rectangle + Area of semi circle

= πr²/2 + l × b + πr²/2

= πr² + l × b

= [22/7 × (3.5)²] + [13 × 7]

= [22/7 × 35/10 × 35/10] + 91

= 38.5 + 91

= 129.5 m²

Perimeter of park = ?

= Perimeter of semi circle + Length of rectangle + Length of rectangle + Perimeter of rectangle

= 2πr/2 + l + l + 2πr/2

= 2πr + 2(l)

= [2 × 22/7 × 3.5] + [2(13)]

= [2 × 22/7 × 35/10] + [26]

= 22 + 26

= 48 m

Therefore, the perimeter of park is 48 m while the area of rectangle is 129.5 m².

Question 4: A flooring tile has the shape of a parallelogram whose base is 24 cm and the corresponding height is 10 cm. How many such tiles are required to cover a floor of area 1080 m²? (If required you can split the tiles in whatever way you want to fill up the corners).

Answer:

Given

Flooring tile in form of parallelogram

base = 24 cm

height = 10 cm

area of floor = 1080 m²

To find

The number of tiles required to cover the floor

Formula

Area of parallelogram = b × h

Working

Area of one tile = ?

= 24 × 10

= 240 cm²

Number of tiles required = ?

= 1080 m²/240 cm²

= 10800000/240

= 1080000/24

= 45000 tiles

Therefore, 45000 tiles would be required to cover the floor whose area is 1080 m².

Question 5: An ant is moving around a few food pieces of different shapes scattered on the floor. For which food-piece would the ant have to take a longer round? Remember, circumference of a circle can be obtained by using the expression c = 2πr, where r is the radius of the circle.

Answer:

a)

Distance covered by the ant to collect food pieces = ?

= 1/2 × 2πr + 2r

= πr + 2r

= 22/7 × 1.4 + 2 × 1.4

= 22/7 × 14/10 + 2.8

= 22/7 × 14/10 + 28/10

= 44/10 + 28/10

= 72/10

= 7.2 cm

b)

Distance covered by the ant to collect food pieces = ?

= 1.5 + 1.5 + 2.8 + 1/2 × 2πr

= 5.8 + πr

= 5.8 + 22/7 × 1.4

= 5.8 + 4.4

= 10.2 cm

c)

Distance covered by the ant to collect food pieces = ?

= 1/2 × 2πr + 2 + 2

= πr + 4

= 22/7 × 1.4 + 4

= 4.4 + 4

= 8.4 cm

Comparing

10.2 cm > 8.4 cm > 7.2 cm

Therefore, for b) food-piece, the ant have to take a longer round.

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