Question

If E, F, G, H, are respectively the mid-points of the sides of a parallelogram ABCD,
area$\left(EFGH\right)=40c{m}^2$, then area(ABCD) is

• A. 40 $c{m}^2$
• B. 20 $c{m}^2$
• C. 80 $c{m}^2$
• D. 60 $c{m}^2$

Answer 1

The correct option is C 80 $c{m}^2$

As shown in figure,

Area of $\Delta DGF$ = $\frac{Areaof\Delta ACD}{4}$

Area of $\Delta EHB$ = $\frac{Areaof\Delta ACB}{4}$

Area of $\Delta AEF$ = $\frac{Areaof\Delta ADB}{4}$

Area of $\Delta GCH$ = $\frac{Areaof\Delta CDB}{4}$

Add all above equation, we get

(Total Area) - (Area of EFGH) = $\frac{TotalArea}{2}$

Total Area = 80 $c{m}^2$