Question

In the given figure, ABCD is a quadrilateral. A line through 'D', parallel to AC, meets BC produced in P. Then:

• A. Area $\left(\Delta ABP\right)$ = Area $\left(quadABCD\right)$
• B. Area $\left(\Delta ABC\right)$ = Area $\left(\Delta ACP\right)$
• C. Area $\left(\Delta BCD\right)$ = Area $\left(quadACPD\right)$
• D. None of the above

Answer 1

The correct option is A Area $\left(\Delta ABP\right)$ = Area $\left(quadABCD\right)$

Here $\Delta DAC$ and $\Delta PAC$ are on the same base AC and between parallel lines AC and DP
$\Rightarrow$ Area $\left(\Delta DAC\right)$ = Area $\left(\Delta PAC\right)$

Adding Area $\left(\Delta ACB\right)$ on both sides, we have,
$\Rightarrow$ Area $\left(\Delta DAC\right)$ + Area $\left(\Delta ACB\right)$
= Area $\left(\Delta PAC\right)$ + Area $\left(\Delta ACB\right)$

$\Rightarrow Area\left(quadABCD\right)=Area\left(\Delta APB\right)$