# 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:** Perimeter of Square `=4xx\text(side)=4xx60=240` metres

Area of Square = Side² `= 60^2 = 3600` square metre

Perimeter of Rectangle = 2(length + breadth)

Or, `240 = 2(80 + text(breadth))`

Or, `80 + text(breadth) = 120`

Or, breadth `= 120-80 = 40` metres

Area of rectangle = length x breadth `= 80 xx 40 = 3200` square metres

Now it is clear that the area of the square field is greater than the area of the rectangular field.

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:** Area of the square plot = Side² `= 25^2 = 625` square metre

Area of the house construction part = length x breadth

`= 20 xx 15 = 300` sq m

So, area of the garden `= 625-300=325` square metre

Cost of developing the garden = Area x Rate

`= 300 xx 55 = 16500` rupees

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:** Area of the rectangular part = length × breadth

`= 20 xx 7 = 140` sq m

Area of Semicircular portions: `=πr^2`

`=(22)/7×3.5^2=11×3.5=38.5` sq m

Perimeter of the shape = Perimeter of circle + 20 + 20

`=2πr+40=2×(22)/7×3.5+40``=22+40=62` m

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 m^{2}? (If required you can split the tiles in whatever way you want to fill up the corners).

**Answer:** Area of the Parallelogram = base x height

`= 24 xx 10 = 240` sq cm

Required number of tiles `=text(Area of floor)/text(Area of tile)`

`=(1080xx100xx100)/(240)=45000`

(area of floor is converted into square cms)

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) Perimeter `=(πd)/(2)+d`

`=(22)/(7)xx(2.8)/(2)+2.8=4.4+2.8=7.2` cm

(b) Perimeter `=(πd)/(2)+2xx\text(breadth)+text(length)`

`=4.4+3+2.8=10.2` cm

(Perimeter of semicircular part is same as in (a))

(c) Perimeter `=(πd)/(2)+2xx\text(slant height)`

`=4.4+4=8.4` cm

So, the food shape in (a) requires the ant to cover the least distance.