Question

If D,E,F are respectively the mid points of the sides BC , CA and AB of $△$ABC and

the area of $△$ ABC is 24 sq. cm, then the area of $△$ DEF is -

• A. 24 $c{m}^2$
• B. 12 $c{m}^2$
• C. 8 $c{m}^2$
• D. 6 $c{m}^2$

Answer 1

The correct option is D

6 $c{m}^2$

Given D, E and F are the mid-points of sides BC, AC and AB respectively of $\Delta$ABC.

Thus, $\Delta$ABC is similar to $\Delta$DEF [by SSS]

$\frac{Area\Delta DEF}{Area\Delta ABC}={\left(\frac{DE}{AB}\right)}^2$

$\frac{Area\Delta DEF}{Area\Delta ABC}={\left(\frac{DE}{2DE}\right)}^2$

Clearly, area ($△$DEF) = $\frac{1}{4}$ area ( $△$ ABC)

= $(\frac{1}{4}\times 24)$ = 6 $c{m}^2$