Question

AD is median of $△ABC$ Area of $△AC$=15 $c{m}^2$ then area of $△ABC$ is

• A. $30c{m}^2$
• B. $22.5c{m}^2$
• C. $15c{m}^2$
• D. $10c{m}^2$

Answer 1

Answer: (A)

$30c{m}^2$

$\Rightarrow$ We know that, the median of a triangle divide it into two triangles of equal area.

$\Rightarrow$ $AD$ is median of $△ABC$.

$\therefore$ $ar\left(△ACD\right)=ar\left(△ABD\right)$

$\therefore$ $ar\left(△ACD\right)=ar\left(△ABD\right)=15c{m}^2$

$\Rightarrow$ Area of $△ABC$ = $ar\left(△ACD\right)+ar\left(△ABD\right)$

$\therefore$ Area of $△ABC$ = $15c{m}^2+15c{m}^2=30c{m}^2$