Question

In the given figure $△FGH$ and $△CDE$ are right angled triangles.

Area of the following shape is ___

$c{m}^2$.

• A. $50c{m}^2$
  
  
• B. $54c{m}^2$
  
• C. $60c{m}^2$
  
  
• D. $64c{m}^2$

Answer 1

The correct option is B $54c{m}^2$



Area ABCDEFGH
=Area (ABEF) +Area (FGH) +Area (CDE)…..(1)
$FH=\sqrt{F{G}^2-G{H}^2}=\sqrt{25-16}=\sqrt{9}=3cm$ [From Pythagorean theorem ]
CE $=\sqrt{D{E}^2-C{D}^2}=\sqrt{25-16}=3cm$
From (1), Area ABCDEFGH $=(6\times 7)+\frac{1}{2}\times 4\times 3+\frac{1}{2}\times 4\times 3$
$=42+6+6=54c{m}^2$