A geometry problem by Fidel Simanjuntak

Geometry Level 3

$BD : DC = 1\text{ cm} : 3 \text{ cm}$ and $AE : EC = 2 \text{ cm}: 1 \text{ cm}$ . The are aof $ADE$ is $50 \text{ cm}^{2}$ .

Find the area of $ABD$ in $\text{cm}^{2}$ .

1 solution

Fidel Simanjuntak
Jul 23, 2016

The area of $CDE$ $= \frac{1}{2} \times$ area of $ADE$

$= \frac{1}{2} \times 50 = 25 cm^{2}$

Area of $ABC$ $= \frac{AC\times BC}{AE\times CD} \times$ area of $ADE$

$= \frac{3\times 4}{2\times 3} \times 50$

$=100 cm^{2}$

Area of $ABD$ = $ABC - ADE - CDE$

$= 100-50-25$

$=25 cm²$