thhe height of an equilateral triangle is 6 cm Find the area of the triangle - Maths -

Question

thhe height of an equilateral triangle is 6 cm Find the area of
the triangle

Shridhar Kaushik · Accepted Answer

Let the side of an equilateral triangle be 'x' cm.We know that the area of an equilateral triangle = $\frac{\sqrt{3}}{4} (s i d e)^{2} = \frac{\sqrt{3}}{4} (x)^{2}$ .... (1)

Also, area of triangle = $\frac{1}{2} \times b a s e \times h e i g h t = \frac{1}{2} \times x \times 6 = 3 x c m^{2}$ .....(2)

On equating (1) and (2), we get

$\frac{\sqrt{3}}{4} (x)^{2} = 3 x \Rightarrow \frac{\sqrt{3}}{4} x = 3 \Rightarrow x = 4 \sqrt{3} c m$

Hence, area of equilateral triangle = $\frac{\sqrt{3}}{4} (s i d e)^{2}$ = $\frac{\sqrt{3}}{4} (4 \sqrt{3})^{2} = \frac{\sqrt{3}}{4} \times 48 = 12 \sqrt{3} c m^{2}$

thhe height of an equilateral triangle is 6 cm. Find the area of the triangle.