Question

In a triangle ABC, E is the mid-point of median AD. Show that ar (ΔBED) = $\frac{1}{4}$ar(ΔABC) [2 MARKS]

Answer 1

Concept : 0.5 Mark
Application : 0.5 Mark
Calculation : 1 Mark

As AD is the median of $△$ABC.It divides $△$ABC into 2 equal triangles.

Area($△$ABD) = $\frac{1}{2}$Area($△$ABC)

Similarly, E is the mid point of AD and BE is the median.

$\therefore$ Area ($△$BED) = $\frac{1}{2}$Area ($△$ABD) = $\frac{1}{4}$Area ($△$ABC)