RS Aggarwal - Mathematics

Book: RS Aggarwal - Mathematics

Chapter: 18. Area of Circle, Sector and Segment

Subject: Maths - Class 10th

Q. No. 15 of Formative Assessment (Unit Test)

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15

In the given figure, an equilateral triangle has been inscribed in a circle of radius 4 cm. Find the area of the shaded region. [Take π = 3.14 and √3 = 1.73]


Radius of circle = R = 4 cm


OD perpendicular to AB is drawn


ΔABC is equilateral triangle,


A = B = C = 60°


OAD = 30°


OD/AO = sin 30°


AO = 4 cm



OD = 1/2 × 4 cm


OD = 2 cm


AD2 = OA2 – OD2


= 42 – 22 = 16 – 4 = 12 cm2


AD = 2√3 cm


AB = 2 × AD


= 2 × 2√3 cm = 4√3 cm


Area of triangle ABC = √3/4 × AB2


= √3/4 × 4√3 × 4√3


= 20.71 cm2


Area of circle = πR2


= 3.14 × 4 × 4 cm2


= 50.24 cm2


Area of shaded region = 29.53 cm2


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