Question

the height of an equilateral triangle is 9underroot3 cm .find its area
$9 \sqrt{3 }$

Answer 1

$height \: o f \: equilateral \: triangle \: \\ \\ = \frac{ \sqrt{3} }{2} \times side \\ \\ side \: = height \times \frac{2}{ \sqrt{3} } \\ \\ side = \frac{9 \sqrt{3} \times 2 }{ \sqrt{3} } \\ \\ side = 18 \: cm \\ \\ area \: = \frac{ \sqrt{3} }{4} \times {side}^{2} \\ \\ = \frac{ \sqrt{3} }{4} \times 18 \times 18 \\ \\ = 81 \sqrt{3} {cm}^{2}$