Question

If AB = BC and area of triangle BEC is 72 $c{m}^2$. Find area of parallelogram if AC = 12 cm.

• A. 288$c{m}^2$
• B. 144$c{m}^2$
• C. 576$c{m}^2$
• D. 216$c{m}^2$

Answer 1

The correct option is A 288$c{m}^2$

Given: AB= BC, AC = 12 cm
Therefore, AC = 2AB
Hence, AB = 6cm
$\text{area of triangle}=\frac{1}{2}\times \text{base}\times \text{height}$
$\Rightarrow 72=\frac{1}{2}\times \text{BC}\times \text{height}$
$\Rightarrow 72=\frac{1}{2}\times 6\times \text{height}$
$\Rightarrow \text{height}=24cm$
$\text{area of parallelogram}=\text{base}\times \text{height}$ $=\text{AC}\times \text{height}$
$\therefore \text{Area of parallelogram}=AC\times \text{height}=12\times 24=288$