Question

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

Answer 1

We know that

Area of square = 1/2(diagonal)²

`"Area of the given kite "= 1/2(32 cm)^2 = 512 cm^2`

Area of 1^st shade = Area of 2^nd shade = 512/2 = 256 cm²

Therefore, the area of paper required in each shape is 256 cm².

For III^rd triangle

Semi-perimeter,

`s=(6+6+8)/2=10 cm`

By Heron’s formula,

`"Area of triangle "=sqrt(s(s-a)(s-b)(s-c))`

`"Area of 3rd triangle "=sqrt(10(10-6)(10-6)(10-8))`

                                `=(sqrt(10xx4xx4xx2))cm^2`

                                `=(4xx2sqrt5)cm^2`

                                `=8sqrt5 cm^2`

                                 = (8 x 2.24) cm²

                                 = 17.92 cm²

Area of paper required for III^rd shade = 17.92 cm²