Question

If $AD$ is median of $△ABC$ and area of $△ACD=15\text{cm}{}^2,$ then area of $△ABC$ is

• A. $30\text{cm}{}^2$
• B. $22.5\text{cm}{}^2$
• C. $15\text{cm}{}^2$
• D. $10\text{cm}{}^2$

Answer 1

The correct option is A $30\text{cm}{}^2$


We know that, the median of a triangle divide it into two triangles of equal area.
$\Rightarrow AD\text{is median of}△ABC$
$\therefore ar(△ACD)=ar(△ABD)=15c{m}^2$
$\Rightarrow \text{Area of}△ABC=ar(△ACD)+ar(△ABD)$
$\therefore \text{Area of}△ABC=15{\text{cm}}^2+15{\text{cm}}^2=30{\text{cm}}^2$