Question

In $△ABC$, $D$ and $E$ are the mid-points of $AB$ and $AC$ respectively, then the area of $△ADE$ is:

• A. $4\times$ Area of $△ABC$
• B. $\frac{1}{4}$ Area of $△ABC$
• C. $2\times$ Area of $△ABC$
• D. $\frac{1}{2}$ Area of $△ABC$

Answer 1

Answer: (B)

$\frac{1}{4}$ Area of $△ABC$

Given :

$D$ and $E$ are the mid-points of $AB$ and $AC$ respectively.

$\therefore$ $2AD=AB$ and $2AE=AC$ ....... $\left(1\right)$

Area of a triangle $=\frac{1}{2}\times$ base $\times$ height

$\therefore$ Area of $△ABC=\frac{1}{2}\times AC\times AB$

Since ADE form a triangle,

$\therefore$ Area of $△ADE=\frac{1}{2}\times AE\times AD$

$=\frac{1}{2}\times \frac{AC}{2}\times \frac{AB}{2}$

$=\frac{1}{4}\times \frac{1}{2}\times AC\times AB$

$=\frac{1}{4}($Area of $△ABC)$

Area of $△ADE=$$\frac{1}{4}($Area of $△ABC)$