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
We know that,
As the diagonals of a square bisect each other at right angle.
Area of given kite = 1/2 (diagonal)2
= 1/2 × 32 × 32 = 512 cm2
Area of shade I = Area of shade II
⇒ 512/2 cm2 = 256 cm2
So, area of paper required in each shade = 256 cm2
For the III section,
Length of the sides of triangle = 6cm, 6cm and 8cm
Semi perimeter of triangle = (6 + 6 + 8)/2 cm = 10cm
Using heron's formula,
Area of the III triangular piece = √s (s-a) (s-b) (s-c)
= √10(10 - 6) (10 - 6) (10 - 8) cm2
= √10 × 4 × 4 × 2 cm2
= 8√6 cm2
