Question

In the given figure, ABCD is a parallelogram. If $ar\left(\Delta AOD\right)=32c{m}^2,$ then $ar\left(\Delta ABP\right)$ will be

• A. $8c{m}^2$
• B. $32c{m}^2$
• C. $16c{m}^2$
• D. $64c{m}^2$

Answer 1

The correct option is B $32c{m}^2$

Since, $\Delta AOD$ and parallelogram ABCD are lying on the same base and between same parallels.
$\Rightarrow area\left(\Delta AOD\right)=\frac{1}{2}$ area (parallelogram ABCD).......(1)
Also, $\Delta ABP$ and parallelogram ABCD are lying on the same base and between same parallels.
$\Rightarrow area\left(\Delta ABP\right)=\frac{1}{2}$ area (parallelogram ABCD).......(2)
From (1) and (2), we get
area of $\Delta ABP$ = area of $\Delta AOD=32c{m}^2$
Hence, the correct answer is option (2).