Question

In an equilateral $△ABC$, if $△DFE$ is formed by joining the midpoints of the sides, the area of $△DFE$ is ___ $\times$ the area of $△$ ABC.

• A. 2
• B. $\frac{1}{3}$
• C. $\frac{1}{4}$
• D. 4

Answer 1

The correct option is C

$\frac{1}{4}$

Given: D, F and E are midpoints of AB, BC and AC respectively.

$\therefore$ $\frac{EF}{AB}=\frac{DE}{BC}=\frac{DF}{AC}=\frac{1}{2}$

$△DFE\sim △ABC$ (By SSS Similarity)

$\Rightarrow$ $\frac{area△DFE}{area△ABC}=\frac{(1{)}^2}{(2{)}^2}$

$\Rightarrow$ $\frac{area△DFE}{area△ABC}=\frac{1}{4}$

$\therefore$$area△DFE=\frac{1}{4}\times area△ABC$