Question

In the given figure, ABCD is a rectangle and ABEF is a parallelogram. Given AB = 16 cm, AD = 10 cm. Find ar($\Delta$ABF)

• A. $80c{m}^2$
• B. $180c{m}^2$
• C. $160c{m}^2$
• D. $90c{m}^2$

Answer 1

The correct option is A $80c{m}^2$

$ar\left(rectangleABCD\right)=AB\times AD$
$=16cm\times 10cm$
$=160c{m}^2$
Since, Parallelograms ABCD and ABEF are lying on same base and between same parallels.
$\Rightarrow ar\left(ABEF\right)=ar\left(ABCD\right)$
$=160c{m}^2$
Now, $ar\left(\Delta ABF\right)=\frac{1}{2}ar\left(ABEF\right)$
$=\frac{1}{2}\times 160c{m}^2$
$=80c{m}^2$
$\Rightarrow ar\left(\Delta ABF\right)=80c{m}^2$
Hence, the correct answer is option (A).