Question

In Figure $ABCD$, find the area of the shaded region.

• A. $220c{m}^2$
• B. $320c{m}^2$
• C. $200c{m}^2$
• D. None of these

Answer 1

The correct option is A $220c{m}^2$

Given: $ABCD$ is a square with side equal to $20cm$,

i.e., $AB=BC=CD=DA=20cm,AF=FB=10cm,DE=8cm$

To find: Area of shaded region.

Solution: Area of square $ABCD=(AB{)}^2={20}^2=400c{m}^2$

Also, we have $AD=20cm$

$\Rightarrow DE+EA=20$

$\Rightarrow 8+EA=20$

$\Rightarrow EA=12cm$

Now, Area of shaded region $=$ Area of square $ABCD-$ Area of $△AEF-$ Area of $△FBC-$ Area of $△EDC$

$=400-\frac{1}{2}\times AE\times AF-\frac{1}{2}\times FB\times BC-\frac{1}{2}\times CD\times DE$

$=400-\frac{1}{2}\times 12\times 10-\frac{1}{2}\times 10\times 20-\frac{1}{2}\times 20\times 8$

$=400-60-100-80$

$=160c{m}^2$