Question

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 figure. How much paper of each shade has been used in it?

Answer 1

ABCD is a square. 

So, AO = OC = OB = OD 

and ∠AOB = 90° [Diagonals of a square bisect each other at right angles] 

BD = 32 cm (Given) ⇒ OA = 32/ 2 cm = 16 cm. 

∆ABD is a right triangle. 

So, area of ∆ABD = 1/ 2 × base × height 

= 1/ 2 × 32 × 16 cm² = 256 cm² 

Thus, area of ∆BCD = 256 cm² 

For triangle CEF, a = b = 6 cm, c = 8 cm. 

∴ s = a + b+ c/ 2=  6+ 6+ 8/ 2 cm = 10 cm

∴ Area of the triangle

Hence, paper needed for shade I = 256 cm², for shade II 

= 256 cm² and for shade III = 17.92 cm² Ans.