Question

In the given figure, If the area of parallelogram BIPS is $144m^2,$
then the area of $\Delta NPSis$ _____.

• A. $144m^2$
• B. $288m^2$
• C. $72m^2$
• D. $36m^2$

Answer 1

The correct option is C $72m^2$

If a triangle and a parallelogram are on the same base and between the same parallels, then the area of the triangle is equal to half the area of the parallelogram.
$\Delta NPS$ and parallelogram BIPS are on the same base SP and between the same parallels SP and IB.
$\therefore ar\left(\Delta NPS\right)=\frac{1}{2}\times ar\left(BIPS\right)$
$=\frac{1}{2}\times 144m^2$
$=72m^2$
Thus, the area of $\Delta NPSis72m^2.$