Question

If $\Delta ABC$ is similar to $\Delta DEF$ such that BC = 3 cm, EF = 4 cm and area of $\Delta ABC=54{cm}^2$. Determine the area of $\Delta DEF$. [4 MARKS]

Answer 1

Concept: 1 Mark
Application: 3 Marks

Since the ratio fo areas of two similar triangles is equal to the ratio of the squares of any two corresponding sides.

$\Rightarrow \frac{Area\left(\Delta ABC\right)}{Area\left(\Delta DEF\right)}=\frac{B{C}^2}{E{F}^2}$

$\Rightarrow \frac{54}{Area\left(\Delta DEF\right)}=\frac{3^2}{4^2}$

$\Rightarrow Area\left(\Delta DEF\right)=\frac{54\times 16}{9}=96c{m}^2$