Question

In a given figure, BE is a median of $△ABD$. If the area of parallelogram ABCD is $24c{m}^2$. Then the area of $△ABE$ is:

• A. $6c{m}^2$
• B. $8c{m}^2$
• C. $12c{m}^2$
• D. $10c{m}^2$

Answer 1

The correct option is A

$6c{m}^2$

In a parallelogram, the triangle between the same parallels and on the same base has an area which is equal to half of that of a parallelogram.

So, area of $△ABD=\frac{1}{2}areaof\left(ABCD\right)$ and BE is a median

Area of $△ABE=\frac{1}{2}areaof△ABD$ (Median divides the triangle into 2 equal parts)

Therefore, area of $△ABE=\frac{1}{4}areaof\left(ABCD\right)=\frac{1}{4}\times 24=6c{m}^2$