Question

Find the area of this figure.

• A. $28{\text{m}}^2$
• B. $22{\text{m}}^2$
• C. $29{\text{m}}^2$
• D. $30{\text{m}}^2$

Answer 1

The correct option is A $28{\text{m}}^2$

Lets name its vertices.
Area of a closed figure = Area of a square BDEF + 2 × Area of $△$ ABD $(\because \text{Area of a}△EGF=\text{Area of a}△ABD)$

$\to$ Area of a square BDEF = side $\times$ side
$=4\times 4=16{\text{m}}^2$
$\text{Area of}△ABD=\frac{1}{2}\times \text{Base}\times \text{Height}$
$\Rightarrow \frac{1}{2}\times BD\times AC=\frac{1}{2}\times 4m\times 3m$
$=6{\text{m}}^2$

Hence, Area of a closed figure $=16{\text{m}}^2+2\times 6{\text{m}}^2=28{\text{m}}^2$

Option (a) is correct.