Question

In the figure below, if DE = 2DC and the area of parallelogram ABDE = 20 square units. Find the area of ΔDBC (in square units).

• A. 10
• B. 4
• C. 5
• D. 6

Answer 1

The correct option is C 5

Drop perpendicular from E on AB and perpendicular from B on DE.
EF=GB, since distance between two opposite sides of a parallelogram is same.

$\text{Area of a parallelogram}=\text{base}\times \text{height}$

Area of the parallelogram ABDE
$=DE\times EF=20$ square units

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

Also, EF = GB

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

$\text{Area of}\Delta DBC=\frac{1}{2}\times DC\times GB=\frac{1}{2}\times \frac{DE}{2}\times EF$
$=\frac{1}{4}\times DE\times EF=(\frac{1}{4}\times 20)\text{sq. units}$
$=5\text{sq. units}$ .
$\therefore$ Area of triangle DBC is $5\text{sq. units}$.