Question

In an equilateral triangle of side 24 cm. a circle is inscribed
touching its sides. The area of the remaining portion of the
triangle is ( V3 =1.732)
​

Answer 1

Inradius of an equilateral triangle

=(side23–√)=2423–√=43–√cm

Area of equilateral triangle

=3–√4×(side)2=3–√4×24×24

=3–√×6×24

=1443–√cm2

144×1.732

=249.408cm2

Now, Area of incircle

=22/7×(Inradius)2

=22/7×4√3×4√3

=22×16×37/7=10567/7

=1150.86cm2

Area of remaining part = area of △ - area of incircle

=249.408−150.86

=98.548cm2