Question

Given that the base of ΔABC , BC = 6 cm. AD is the median of ΔABC with E at the mid point of AD. If altitude of ΔABC is 8 cm, the area of ΔBED is______

• A. 24 $c{m}^2$
• B. 4 $c{m}^2$
• C. 12 $c{m}^2$
• D. 6 $c{m}^2$

Answer 1

The correct option is D 6 $c{m}^2$

Median divides a triangle into 2 triangles of equal area.

In $△$ABC, AD is the median.So,
Area of $△$ABD = Area of $△$ADC
$\Rightarrow$Area of $△$ABD = $\frac{1}{2}$$\times$Area of $△$ABC...(i)

Again consider $△$ABD. Here, BE is the median .
So, Area of $△$BED = Area of $△$ABE...(ii)

As, Area of $△$ABD
=Area of $△$BED + Area of $△$ABE
=2 x Area of $△$BED ...from(ii)
$\Rightarrow$Area of $△$BED = $\frac{1}{2}$$\times$Area of $△$ABD
= $\frac{1}{2}\times \frac{1}{2}$ Area of $△$ABC
= $\frac{1}{4}$ (Area of $△$ABC)
= $\frac{1}{4}\times \frac{1}{2}$ (6 × 8) = 6 $c{m}^2$