Question

In an eauilateral triangle of side 12 cm, a circle is inscribed touching its sides. Find the area of the
portion of the triangle not included in the circle. Take 13 = 1.73 and %= 314.​

Answer 1

Area of equilateral triangle=√3/4.side^2 = √3/4×(12)^2 =36√3cm^2.

Semi perimeter (s) of the triangle. =( 12+12+12)/3 = 18 cm.

Radius. (r) of the in circle = area of ∆/semi perimeter of ∆

r = 36√3/18 = 2√3 cm.

Area of in circle= π.r^2= 3.14×(2√3)^2 = 3.14×12 = 37.68 cm^2.

Required area = area of the triangle -area of in circle.

= 36√3 - 37.68. = 36×1.732 - 37.68

= 62.352 - 37.68

=24.672 cm^2. Answer.