Question

In fig, D,E,F are the mid points of sides BC,CA and AB, if ar ($△$ABC) =28${cm}^2$, then ar (AEDF) =

• A. 21${cm}^2$
• B. 18${cm}^2$
• C. 16${cm}^2$
• D. None of these

Answer 1

The correct option is D None of these

F,E are midpoints of the sides AB and AE.

respectively.

$\therefore FE=BD=DC=\frac{1}{2}BC$ and $FE/BC$.

$DE$ is its diagonal .

$\therefore$ area of $\Delta BDF$ = area of $\Delta DEF$

Similarly we can prove area of $\Delta DEC$ = area of $\Delta DEF$

area of $\Delta AEF$ = area of $\Delta ADEF$

But area $\Delta BDF+$ area of $\Delta DEC+$ area of $\Delta AEF+$ area of $\Delta DEF$ = area of $\Delta ABC$

i.e (area of $\Delta DEF$) = area of $\Delta ABC$

area of $\Delta DEF=\frac{1}{4}$ area of $\Delta ABC$

area of $\Delta DEF=\frac{56}{4}=14c{m}^2$