An equilateral triangle has side 12 cm. A circle is drawn inside it touching all three sides. Find the area of that circle in ${\text{cm}}^2$. Take π = 3.14.

The triangle's area = (√3/4) × 144 = 36√$3{\text{cm}}^2$ and its perimeter is 36 cm, so the radius of the touching circle = area ÷ (half the perimeter) = 36√3/18 = 2√3 cm. Then $r^2=12$ and the area = $3.14\times 12=37.68{\text{cm}}^2$. (The circle through the three corners has twice that radius, $r^2=48$, giving $150.72{\text{cm}}^2.$)