Question

If AB = BC, AC=12 cm, and area of Δ BEC is 72 $c{m}^2$, find area of parallelogram ACEF.

• 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,
area of Δ BEC = 72 $c{m}^2$
AC = 12 $cm$
∴ AC = 2AB
$\Rightarrow$AB = 6 $cm$
$\text{area of Δ BEC}=\frac{1}{2}\times \text{base}\times \text{height}$
$\Rightarrow 72=\frac{1}{2}\times \text{BC}\times \text{height}$
$\Rightarrow 72=\frac{1}{2}\times 6\times \text{height}$
$\Rightarrow \text{height}=24cm$
Hence,
$\text{Area of parallelogram}=\text{base}\times \text{height}$ $=\text{AC}\times \text{height}=12\times 24=288c{m}^2$