Question

The altitude of an equilateral triangle having 3√3 cm find area​

Answer 1

Given:

• Altitude = 3√3 cm

To find:

• Area of triangle = ?

Method:

Let a be the side of an equilateral triangle

$\sf{Height \: of \: Equilateral \: triangle = \dfrac{ \sqrt{3} }{2} a} \\ \implies \sf height = \dfrac{ \sqrt{3} }{2} a \\ \implies \sf{3 \sqrt{3} = \frac{ \sqrt{3} }{2} a} \\ \\ \sf \: cancelling \sqrt{3} \: on \: both \: sides\\ \implies \sf{3 = \frac{1}{2} a} \\ \implies \sf{ \frac{a}{2} = 3} \\ \implies \boxed{ \sf{a = 6}}$

Side = 6 cm

Height = 3√3 cm

$\sf{area \: of \: triangle = \dfrac{1}{2} \times base \times height } \\ \implies \sf{area = \frac{1}{2} \times6 \times 3 \sqrt{3 } } \\ \\ \implies \sf{area =3 \times 3 \sqrt{3} } \\ \implies \boxed{ \sf{area = 9 \sqrt{3} \: {cm}^{2} }}$

Area = 9√3 cm²