Question

ABC is a triangle in which D is the mid-point of BC. E and F are mid-points of DC and AE respectively. If ar($△$ABC) = 16 $c{m}^2$, then
ar($△$DEF) is

• A. 1 $c{m}^2$
• B. 2 $c{m}^2$
• C. 4 $c{m}^2$
• D. 8 $c{m}^2$

Answer 1

The correct option is B 2 $c{m}^2$

Median divides the triangle into two equal areas.
Area $\left(△DEF\right)$ = $\frac{1}{2}Area\left(△ADE\right)$ = $\frac{1}{2}\times \frac{1}{2}$$\left(Area△ADC\right)$ = $\frac{1}{4}\times \frac{1}{2}$$\left(Area△ABC\right)$
= $\frac{1}{8}\times 16$
= $2c{m}^2$