Question

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

• A. $\frac{1}{4}$ar(ΔABD)
• B. $\frac{1}{4}$ar(ΔABC)
• C. $\frac{1}{4}$ar(ΔBCD)
• D. $\frac{1}{4}$ar(ΔACB)

Answer 1

The correct option is B

$\frac{1}{4}$ar(ΔABC)

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

Area(△ABD) = 12Area(△ABC)

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

∴ Area (△BED) = 12Area (△ABD) = 14Area (△ABC)