Question

In the figure shown, the area of the parallelogram shown is 60 $c{m}^2$. If E,F,G,H are mid-points of sides of parallelogram ,then area of the EFGH is______

• A. 15 $c{m}^2$
• B. 30 $c{m}^2$
• C. 60 $c{m}^2$
• D. 120 $c{m}^2$

Answer 1

The correct option is B 30 $c{m}^2$

Join the line HF as shown.

Area of parallelogram HFBA = $\frac{1}{2}$ of Area of ABCD = 30 $c{m}^2$

ΔHFE and parallelogram HFBA are between same parallel lines and are on the same base.

So, Area of ΔHFE = $\frac{1}{2}$ of area of parallelogram HFBA

= 15 $c{m}^2$

Similarly, Area of ΔHFG = 15 $c{m}^2$

So, required area = Area of ΔHFE + Area of ΔHFG = 30 $c{m}^2$