Question

In the given figure ABCD is a parallelogram. F is a point on DC and FE is the median of $\Delta ABF$. If area of $\Delta AFE$ is $15c{m}^2$, then the area of parallelogram ABCD is

• A. $30c{m}^2$
• B. $45c{m}^2$
• C. $60c{m}^2$
• D. $150c{m}^2$

Answer 1

The correct option is C

$60c{m}^2$

FE is the median of ABF...... (given)

Area of $\Delta ABF=2\times \Delta AFE$ ..... (median divides a triangle into two triangles of equal area) $\Delta ABF=30c{m}^2$

Area of parallelogram $ABCD=2\times \Delta ABF$…… (area of parallelogram is twice the area of triangle,if both are on the same base and between the same parallels)

Area of parallelogram ABCD $=2\times 30=60c{m}^2$

Hence (C)