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Segment AB measures 4 cm and is a diameter of circle P. In triangle ABC, point C is on circle P and BC = \(1\) cm. What is the area of the shaded region?

 

 Apr 23, 2022
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ABC forms a right triangle  with a leg of  1  and a hypotenuse of  4

The other leg =  sqrt (4^2  - 1^2 ) =  sqrt (15)

 

The area of this  triangle =  product of the leg lengths  /  2  =  (1/2)(1) (sqrt 15)  =  sqrt 15 / 2

 

Area of the circle =      pi (AP)^2  = pi * 2^2   =  4pi

 

So.....the shaded region is [ 4pi - sqrt (15)  / 2 ] cm^2   ≈ 10.63 cm ^2

 

cool cool cool

 Apr 23, 2022

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