Question

The one side of an equilateral triangle is 6cm. Find its altitude.​

Answer 1

$a = \frac{ \sqrt{3} }{4} \times {side}^{2} \\ a = \frac{ \sqrt{3} }{4} \times {6}^{2} \\ a = \frac{ \sqrt{3} }{4} \times 36 \\ a = 9 \sqrt{3} \: {cm}^{2}$

now using altitude formula

area of triangle =

$\frac{1}{2} \times base \times height \\ = \frac{1}{2} \times 6 \times h$

or

$9 \sqrt{3 } = \frac{1}{2 } \times 6 \times h$

$h = \frac{9 \sqrt{3} \times 2 }{6} \\ h = 3 \sqrt{3} cm$