Question

In the figure given below, ABCD is a parallelogram. ABE is a right-angled triangle whose area is 32 cm${}^2$. Find the area of the parallelogram.

• A. $128c{m}^2$
• B. $32c{m}^2$
• C. $320c{m}^2$
• D. $224c{m}^2$

Answer 1

The correct option is D $224c{m}^2$

Given:
$\Delta$ABE is a right-angled triangle, and its area is 32 cm${}^2$.

$\Rightarrow \frac{1}{2}\times AE\times BE=32\Rightarrow \frac{1}{2}\times AE\times 4=32\Rightarrow AE=16cm$

$\text{Area of a parallelogram}=\text{Base}\times \text{Height}$

If BD is taken as the base in ABCD, then AE will be its height.

$\therefore Area=AE\times BD$
$=16\times (4+10)$
[$\because$ BD = BE + ED]
$=16\times 14$
$=224c{m}^2$

Hence, the area of the parallelogram is 224 cm${}^2.$