Question

In the given figure, ABCD is a square with diagonal 44cm. How much paper of each shade is needed to make a kite given in the figure.

Answer 1

We know that

Area of square sheet ABCD = ½ × diagonal²

By substituting the value

Area of square sheet ABCD = ½ × 44 × 44 = 968 cm²

From the figure we know that the

Area of yellow sheet = Area of region I + Area of region II

It can be written as

Area of yellow sheet = ½ × Area of square sheet ABCD

By substituting the value

Area of yellow sheet = ½ × 968 = 484 cm²

From the figure we know that the

Area of red sheet = Area of region IV

It can be written as

Area of red sheet = 1/4 × Area of square sheet ABCD

By substituting the value

Area of red sheet = 1/4 × 968 = 242 cm²

Consider △ AEF

We know that AE = 20cm, EF = 14cm and AF = 20cm

Consider a = 20cm, b = 14cm and c = 20cm

So we get

From the figure we know that

Area of green sheet = Area of region III + Area of region V

It can be written as

Area of green sheet = ¼ × Area of square sheet ABCD + 131.25

By substituting the values

Area of green sheet = ¼ × 968 + 131.25

On further calculation

Area of green sheet = 242 + 131.25

By addition

Area of green sheet = 373.25 cm²

Therefore, the area of yellow sheet is 484 cm², area of red sheet is 242 cm² and the area of green sheet is 373.25cm².