Question

If the perimeter of an equilateral triangle is $36cm$, calculate its area and height.

Answer 1

Perimeter$=3x=36$cm

$x=12$cm

In $\Delta$ABD by Pythagoras theorem

$x^2=(x/2{)}^2+A{D}^2$

$A{D}^2=\frac{3x^2}{4}$

$\Rightarrow AD=\frac{\sqrt{3}}{2}x$

height $=\frac{\sqrt{3}}{2}\times 12=6\sqrt{3}$cm

area $=\frac{1}{2}\times$base$\times$height

$=\frac{1}{2}\times x\times \frac{\sqrt{3}}{2}x$

$=\frac{\sqrt{3}}{4}{x}^2=\frac{\sqrt{3}}{4}\times (12{)}^2$

Area $=36\sqrt{3}c{m}^2$.