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 area of $△ABC$ is $16c{m}^2$ Find the ara of $△DEF.$

Answer 1

In $△ABC,$ D is midpoint of BC. E and F are the midpoints of DC and AE respectively.

Area of $△ABC=16c{m}^2$
FD is joined.

$\because$ D is the midpoint of BC
$\therefore$ AD is the median and median divides the triangle into two triangles equal in area.
Area of $△ADC=\frac{1}{2}ar\left(△ABC\right)$
$=\frac{1}{2}\times 16=8c{m}^2$
Similarly, E is the midpoint of DC
$\therefore area\left(△ADE\right)=\frac{1}{2}ar\left(△ADC\right)=\frac{1}{2}\times 8=4c{m}^2$

$\because$ F is mid point of AE of $△ADE$

$\therefore$ ar$△DEF$ = $\frac{1}{2}$ Area $△ADE=\frac{1}{2}\times 4=2c{m}^2$