Question

In a circular table cover of radius 32 cm, a design is formed Leaving an equilateral triangle ABD in the middle. Find the area of the remaining part

Answer 1

Hi there!

Radius of 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 = πR² = 22/7 × 32 × 32 = 22528/7 cm²

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

                              = (22528/7 - 768√3) cm²

Hence,

Area of Shaded region = (22528/7 - 768√3) cm²

Cheers!

Answer 2

Answer:

Plzz go through the below image

Step-by-step explanation: