Krishna
0

Step 1:  Set up a formula to calculate radius of the inscribed circle to an equilateral triangle.

NOTE: Let r be the radius the inscribed circle to an equilateral triangle of

side a, then

r = a * \frac{\sqrt{3}}{6}

Step 2: Find the area of the inscribed circle

NOTE:  Area of the circle = \pi r^2

= \pi (a * \frac{\sqrt{3}}{6})^2

= \pi \frac{a^2}{12} ........................(1)

Step 3; Find the side of the equilateral triangle by using the area formula

NOTE:  Area of the equilateral triangle A= a^2 \frac{\sqrt{3}}{4}

Area A = 100 cm^2

So,  100 =   a^2 \frac{\sqrt{3}}{4}

a^2 = 100 * \frac{4}{\sqrt{3}}

Step 4:  Substitute a^2 into expression of the area

NOTE: A\ =\ \pi\ \frac{\frac{400}{\sqrt{3}}}{12}    Since equation (1)  (See step 2)

=   \pi \frac{100 \sqrt{3}}{9}