Question

An equilateral triangle is inscribed in a circle of radius 10 cm10 cm. Find the area of the triangle.

Answer 1

Consider the diagram shown below.

Here,

$a=10cm$

Now, we know that,

$\frac{h}{a}=\sin 30{}^{\circ }$

$h=\frac{10}{2}=5cm$

Also,

$\frac{S}{2\times 10}=\cos 30{}^{\circ }$

$S=10\sqrt{3}cm$

So, the height of the triangle is,

$\Rightarrow a+h=10+5=15cm$

Therefore,

Area of the triangle $=\frac{1}{2}\times 10\sqrt{3}\times 15=75\sqrt{3}c{m}^2$

Hence, this is the required result.