Question

In the figure below, if $DE=2DC$ and the area of parallelogram ABDE = 20 cm${}^2$, find the area of $\Delta DBC$.

• A. 10 cm${}^2$
• B. 4 cm${}^2$
• C. 5 cm${}^2$
• D. 6 cm${}^2$

Answer 1

The correct option is C

5 cm${}^2$

Area of a parallelogram = base $\times$ height
Area of the parallelogram ABDE = DE $\times$ EF = 20 cm${}^2$

Given, DE = 2DC

$\Rightarrow$ DC = $\frac{DE}{2}$

Area of $\Delta DBC$ = $\frac{1}{2}\times$ base $\times$ height

= $\frac{1}{2}\times$ DC $\times$ EF

= $\frac{1}{2}\times \frac{DE}{2}\times EF$

= $\frac{1}{4}\times DE\times EF$

= $\frac{1}{4}\times$ Area of parallelogram ABDE

= $\frac{1}{4}\times 20$ = 5 cm${}^2$