Question

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

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

Answer 1

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

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

$\Delta DGF+\Delta EHB+\Delta AEF+\Delta GCH=\frac{TotalArea}{2}$

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

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

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