Question

In the following figure, seg DH $\perp$ seg EF and seg GK $\perp$ seg EF. If $DH=18cm$, $GK=30cm$ and $A\left(\Delta DEF\right)=300c{m}^2$, then find:
(i) $EF$
(ii) $A\left(\Delta GEF\right)$
(iii) $A\left(\square DEFG\right)$.

Answer 1

Area of a triangle = $\frac{1}{2}\times base\times height$.

For $\Delta DEF$, $EF$ is base and $DH$ is height.

Hence, $A\left(\Delta DEF\right)=\frac{1}{2}\times EF\times DH$.

i) That gives, $EF=2\times \frac{A\left(\Delta DEF\right)}{DH}$

$EF=2\times \frac{450}{18}$

$EF=50cm$

ii) $A\left(\Delta GEF\right)$ $=0.5\times GK\times EF$

$=0.5\times 30\times 50$

$=750c{m}^2$

iii) $A\left(\square DEFG\right)=A\left(\Delta DEF\right)+A\left(\Delta GEF\right)$

$=450+750$

$=1200c{m}^2$