Q. 63.7( 330 Votes )

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 (shaded region).


Answer :

Radius of the circle "R" = 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 [ By the property of equilateral triangle inscribed in a circle]

⇒ 2/3 AD = 32 cm

⇒ AD = 48 cm
In ΔADB,

image

By Pythagoras theorem,

AB= AD2  + BD2 

⇒ AB= 482  + (AB/2)2

⇒ AB= 2304  + AB2/4
⇒ 3/4 (AB2) = 2304

⇒ AB= 3072

⇒ AB = 32√3 cm
Area of ΔABC = √3/4 × (32√3)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 ΔABC

                              = (22528/7 - 768√3) cm2

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Quiz | Area Related with Circles47 mins
Quiz | Imp. Qs. on Circles37 mins
Quiz | Testing Your Knowledge on Circles32 mins
Short Cut Trick to Find Area of Triangle43 mins
Champ Quiz | Area Related with the Circle45 mins
Tricks to MemoriseFREE Class
Smart and Effective study is the Key of success45 mins
Trigonometric Identities44 mins
Various Tricks for How to Study Effectively32 mins
How To Give Dynamic Input to JAVA program?63 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses