Question

D, E, F are midpoints of BC, CA and AB respectively. G, H, I are midpoints of FE, FD, DE respectively. Areas of $\Delta DHI$ and $\Delta AFE$ are in the ratio

• A. 1 : 3
• B. 1 : 4
• C. 1 : 9
• D. 1 : 16

Answer 1

The correct option is B 1 : 4

We have area of triangle $AFE=\frac{A}{4}$. (If A = Area of triangle ABC) and area of triangle $DHI=\frac{\left(\frac{A}{4}\right)}{4}=\frac{A}{16}.$
Hence, ratio = 1 : 4.