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# 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.Q6

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What is the solution of ncert class 10 chapter areas related to circles , how i solve this question in a easiest and simplest way . Find the best solution of exercise 12.3 question no. 6 , sir please help me to solve this question in a easiest way.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

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1. Radius of the circle = 32 cm

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

â‡’ BD = AB/2

Since, AD is the median of the triangle

By Pythagoras theorem,

â‡’ AB2Â = 482+(AB/2)2

â‡’ AB2Â = 2304+AB2/4

â‡’ 3/4 (AB2)= 2304

â‡’ AB2Â = 3072

â‡’ AB= 32âˆš3 cm

Area of Î”ADB = âˆš3/4 Ã—(32âˆš3)2Â cm2Â = 768âˆš3 cm2

Area of circle = Ï€R2Â = (22/7)Ã—32Ã—32 = 22528/7 cm2

Area of the design = Area of circle â€“ Area of Î”ADB

= (22528/7 â€“ 768âˆš3) cm2

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