Question

If D, E, F are the midpoints of sides BC, CA and AB of $△$ ABC, then the ratio of the area of $△$ DEF to $△$ ABC is:

• A. 1: 4
• B. 1: 2
• C. 2: 3
• D. 4: 5

Answer 1

The correct option is A

1: 4

D, E, F are the midpoints of sides BC, CA and AB of $△$ABC ...(given)

Hence, $\frac{DE}{AB}=\frac{FE}{BC}=\frac{FD}{AC}=\frac{1}{2}$ .... (SSS Similarity)

$△DEF\sim △ABC$

$\frac{area\left(\Delta DEF\right)}{area\left(\Delta ABC\right)}={\left(\frac{DF}{AC}\right)}^2={\left(\frac{1}{2}\right)}^2=\frac{1}{4}$