Question

In the given figure, $AS||DC,AD||EG||HF||SC.Ifar\left(\Delta ADE\right)+ar\left(\Delta GEF\right)+ar\left(\Delta HSC\right)is50c{m}^2$ , then the area of quadrilateral ASCD is equal to

• A.
  $75c{m}^2$
• B.
  $80c{m}^2$
• C.
  $100c{m}^2$
• D.
  $120c{m}^2$

Answer 1

The correct option is C

$100c{m}^2$


Given that$Ar\left(\Delta ADE\right)+Ar\left(\Delta GEF\right)+Ar\left(\Delta HBC\right)=50c{m}^2$

We know that if a parallelogram and a triangle are on the same base and between the same parallels, then area of triangle is half the area of the parallelogram.

$\Rightarrow \frac{1}{2}Ar\left(ADEG\right)+\frac{1}{2}Ar\left(GEFH\right)+\frac{1}{2}Ar\left(HBCF\right)=50c{m}^2\Rightarrow Ar\left(ADEG\right)+Ar\left(GEFH\right)+Ar\left(HBCF\right)=100c{m}^2\Rightarrow Ar\left(ABCD\right)=100c{m}^2$

Hence, the correct answer is option (c).