A kite in the shape of a square with a diagonal 32 cm and an isosceles triangle of base 8 cm and sides 6 cm each is to be made of three different shades as shown in Fig. 12.17. How much paper of each shade has been used in it?

 

Solution:

As the kite is in the shape of a square, its area will be

A = (½)×(diagonal)2

Area of the kite = (½)×32×32 = 512 cm2.

The area of shade I = Area of shade II

512/2 cm2 = 256 cm2

So, the total area of the paper that is required in each shade = 256 cm2

For the triangle section (III),

The sides are given as 6 cm, 6 cm and 8 cm

Now, the semi perimeter of this isosceles triangle = (6+6+8)/2 cm = 10 cm

By using Heron’s formula, the area of the III triangular piece will be

=

= √[10(10-6)(10-6)(10-8)] cm2

= √(10×4 ×4×2) cm2

= 8√5 cm2 = 17.92 cm2 (approx.)