Question

In the given figure, if area of parallelogram $ABEF$ is $96c{m}^2$; state giving reason, the area of $△ADB$.

• A. $48c{m}^2$
• B. $38c{m}^2$
• C. $58c{m}^2$
• D. $68c{m}^2$

Answer 1

The correct option is A $48c{m}^2$

We know that area of a parallelogram $=$ base $\times$ height
Area of parallelogram $ABEF=AB\times \text{height}$
and Area of parallelogram $ABCD=AB\times \text{height}$
In the figure the height of the both the parallelogram are equal.
Thus, Area of parallelogram $ABCD=$ Area of parallelogram $ABEF=96c{m}^2$
We know that the diagonal bisects the parallelogram into two equal triangles.
Thus, area of $△ADB=\frac{1}{2}\times$ area of parallelogram $ABCD$
$=\frac{1}{2}\times 96$
$=48c{m}^2$