Question

Question 118

A design is made up of four congruent right triangles as shown in the given figure. Find the area of the shaded portion.

Answer 1

Area of one right triangle $=\frac{1}{2}\times BH\times BG=\frac{1}{2}\times 10\times 30=150c{m}^2$
So, area of 4 right angled triangles $4\times 150=600c{m}^2$
[$\because$ all the right angled triangles are congruent here]
$\because$ Area of square = $(Side{)}^2$ [GC = 10 cm, because all the triangles are congruent]
Area of ABCD = $(30+10{)}^2={40}^2=1600c{m}^2$
$\therefore$ Area of shaded portion $=1600-600=1000c{m}^2$