Question

Find the height of an equilateral triangle having side 2a.

Answer 1

Area of an equilateral

$\Delta =\frac{\sqrt{3}}{4}{A}^2$

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

Area $=\sqrt{3}{a}^2$

$AD=h=$ height

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

$\sqrt{3}{a}^2=\frac{1}{2}\times 2a\times h$

$\therefore h=\sqrt{3}a$