Question

ABCD is a parallelogram and E and F are mid-points of AD and BC respectively. P is any point on AB. If area of ΔEDF = 16 $c{m}^2$, then find the area of ( ΔAEP+ ΔBFP)

• A. 16 $c{m}^2$
• B. 20$c{m}^2$
• C. 26 $c{m}^2$
• D. 30 $c{m}^2$

Answer 1

The correct option is A 16 $c{m}^2$

Given that area of ΔDEF = 16 $c{m}^2$

ΔDEF and parallelogram DEFC are on same bases (DE) and same parallels (DE and CF)
So, ar (||gm DEFC)= 2 $\times$ ar of ΔDEF = 32 $c{m}^2$

As E and F are mid points of AD and BC,
ar (||gm DEFC) = ar(||gm EABF)= 32 $c{m}^2$

Again triangle PEF and parallelogram EABF are on same bases (EF) and same parallels.

So, $ar\left(\Delta PEF\right)=\frac{1}{2}\times ar\left(||gmEABF\right)=16c{m}^2$

Now,
ar (ΔAEP) + ar (ΔPFB) + ar (PEF) = ar(||gm EABF)
$\Rightarrow$ ar (ΔAEP) + ar (ΔPFB) + 16 = 32

$\therefore$ ar (ΔAEP) + ar (ΔPFB) = 16 cm${}^2$