Question

In a circular table cover of radius $323cm$, a design is formed leaving an equilateral triangle $ABC$ in the middle as shown in fig. $12.24$. Find the area of the design (shaded region).

Answer 1

For an equilateral triangle inscribed in circle,

side = radius $=323cm=3.23m$

Area of $\Delta ABC=\frac{\sqrt{3}}{4}(side{)}^2=4.5175sq.m$

Area of circle $=\pi r^2=32.7759sq.m$

$\therefore$ Area of design = Area of circle - Area of $\Delta ABC$

$=(32.7759-4.5175)$ sq. m

$=28.26$ sq. m