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
Fig. 12.24. Find the area of the design
​

Answer 1

 ANSWERS::

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√3cm

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

I HOPE ALL U UNDERSTOOD