Question

If the altitude of equilateral traingle is 5 cm ,then its area ?

Answer 1

Step-by-step explanation:

Let the side of equilateral triangle x cm and height be h cm.

$\therefore \: h = \frac{ \sqrt{3} }{2} \times x \\ \therefore \: 5 = \frac{ \sqrt{3} }{2} \times x \\ \therefore \: x = \frac{10}{ \sqrt{3} } \\ Area \: of \: equilateral \: \triangle \: = \frac{ \sqrt{3} }{4} \times {x}^{2} \\ = \frac{ \sqrt{3} }{4} \times {( \frac{10}{ \sqrt{3} }) }^{2} \\ = \frac{ \sqrt{3} }{4} \times {\frac{100}{ 3}} \\ = \frac{25 \sqrt{3} }{3} \\ thus \\ Area \: of \: equilateral \: \triangle \: = \frac{25 \sqrt{3} }{3} \: {cm}^{2}$