##### 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:

Side of square = 60 m

Perimeter of square = 4 × side

= 4 × 60 = 240 m

Length of rectangle = 80 m

Perimeter of rectangle = Perimeter of square

2 (a + b) = 240

2 (80 + b) = 240

160 + 2b = 240

2b = 240 – 160 = 80

$\Rightarrow $ b = 40

$\therefore $ Breadth of rectangle = 40 m

Now, area of square = (side)^{2}

= (60)^{2} = 3600 m^{2}

Area of rectangle = a × b

= 80 × 40 = 3200 m^{2}

$\therefore $ Square has the 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 ₹ 55 per m^{2}.

##### Answer:

Side of square plot = 25 m

Area of square plot = (side)^{2}

= (25)^{2} = 25 × 25 = 625 m^{2}

Length of house = 20 m

Breadth of house = 15 m

Area of house = 20 × 15 = 300 m^{2}

$\therefore $ Area of Garden = Area of Plot – Area of house

= 625 – 300 = 325 m^{2}

Cost of developing the garden at the rate of

₹ 55 per m^{2}

= 325 × 55 = ₹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 = 20 – (3.5 + 3.5) = 13 metres].

##### Answer:

##### 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}?

##### Answer:

##### 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.