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 figure find the area of the design​

Answer 1

Radius of the circle = 32 cm

Draw a median AD of the triangle passing through the centre of the circle.

⇒ BD = AB/2

Since, AD is the median of the triangle

∴ AO = Radius of the circle = 2/3 AD

⇒ 2/3 AD = 32 cm

⇒ AD = 48 cm

In ΔADB,

By Pythagoras theorem,

AB2 = AD2 + BD2

⇒ AB2 = 482 + (AB/2)2

⇒ AB2 = 2304 + AB2/4

⇒ 3/4 (AB2) = 2304

⇒ AB2 = 3072

⇒ AB = 32√3 cm

Area of ΔADB = √3/4 × (32√3)2 cm2 = 768√3 cm2

Area of circle = π R2 = 22/7 × 32 × 32 = 22528/7 cm2

Area of the design = Area of circle - Area of ΔADB

= (22528/7 - 768√3) cm2