Question

In the given figure, ABCD is a parallelogram. P and Q are midpoints of AB and AD respectively. If the area of parallelogram ABCD is $20c{m}^2$, then the area of $\Delta APQ$ is

• A. $2.5c{m}^2$
• B. $5c{m}^2$
• C. $10c{m}^2$
• D. $40c{m}^2$

Answer 1

The correct option is A

$2.5c{m}^2$

ABCD is a parallelogram .... (given)

Area $\Delta ABD=\frac{1}{2}$ of area of parallelogram ABCD ....(diagonal divides a parallelogram into two triangles of equal area)

Area $\Delta ABD$ $=\frac{1}{2}\times 20=10c{m}^2$

Area $\Delta ABQ=\frac{1}{2}$ Area $\Delta ABD$ .... (median divides a triangle into two triangles of equal area)
$=\frac{1}{2}\times 10=5c{m}^2$

Area $\Delta APQ=\frac{1}{2}$ Area $\Delta ABQ$ ..... (median divides a triangle into two triangles of equal area)
$=\frac{1}{2}\times 5=2.5c{m}^2$