Question

In a triangle $ABC,D$ and $E$ are the midpoints of $AB$ and $AC$ respectively. If the area of triangle $ABC=60$ sq cm., then the area of the $△ADE$ is equal to:

• A. $15$ sq cm
• B. $20$ sq cm
• C. $25$ sq cm
• D. $30$ sq cm

Answer 1

The correct option is A $15$ sq cm

Refering figure,
$DE=\frac{1}{2}BC$
and $AP=\frac{1}{2}AQ$
Given, Area of $\Delta ABC=60c{m}^2$
or $\frac{1}{2}\times BC\times AQ=60$
or $BC\times AQ=120$
$\therefore$ Area of $\Delta ADE=\frac{1}{2}DE\times AP$
$=\frac{1}{2}\times \frac{1}{2}BC\times \frac{1}{2}AQ=\frac{1}{8}BC\times AQ$
$=\frac{1}{8}\times 120=15sq.cm.$