Question

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

Answer 1

Given:

Diagonal $=32cm$ , Base$=8cm$ , side$=6cm$

$\Rightarrow$Area of square

$=\frac{1}{2}\times {\left(d\right)}^2$

$=\frac{1}{2}\times {\left(32\right)}^2=512{cm}^2$

$\Rightarrow$Area of shaded portion $I=$ Area of shaded portion $II$

$\Rightarrow$ $\frac{512}{2}=256{cm}^2$

$\therefore$ Area of paper required $=256{cm}^2$

$\Rightarrow$For triangle $III$ region

$\Rightarrow$$S=\frac{6+6+8}{2}=10cm$

$\Rightarrow A=\sqrt{s(s-a)(s-b)(s-c)}$

$\Rightarrow$Area $=\sqrt{10(10-6)(10-6)(10-8)}=\sqrt{10\times 4\times 4\times 2}{cm}^2$

$\Rightarrow$$A=4\times 2\sqrt{5}{cm}^2=17.92{cm}^2$

Area of paper required for $III$ triangle shade$=17.92{cm}^2$