Question

In a circular table cover of radius 32 cm, a design is formed leaving an equilateral triangle ABC in the middle as shown in the given figure. Find the area of the design (Shaded region). [Use Π = 22/7]

Answer 1

Radius (r) of circle = 32 cm

AD is the median of ΔABC.

`AO =2/3 AD = 32`

AD = 48 cm

In ΔABD,

AB² = AD² + BD²

`AB^2 = (48)^2 + ((AB)/2)^2`

`(3AB^2)/4 = (48)^2`

`AB = (48xx2)/sqrt3 = 96/sqrt3`

`= 32sqrt3 cm`

Area of equilateral triangle ΔABC = `sqrt3/4(32sqrt3)^2`

`=sqrt3/4 xx 32xx32xx2 = 96xx8xxsqrt3`

`= 768sqrt3 cm^2`

Area of circle = πr²

`= 22/7xx(32)^2`

`=22/7 xx 1024`

`= 22528/7 cm^2`

Area of design = Area of circle − Area of ΔABC

`= ((22528)/7 - 768sqrt3) cm^2`