We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.
 
+0  
 
0
249
1
avatar

Segment $AB$ measures 4 cm and is a diameter of circle $P$. In triangle $ABC$, point $C$ is on circle $P$ and $BC = 2$ cm. What is the area of the shaded region?

 

 Jun 27, 2018
 #1
avatar+100588 
+1

Since the base of triangle  ACB  is a diameter, then  ACB  is a right angle

And we can use the Pythagorean Theorem to find  AC

 

AC =  √[AB^2  - BC^2]  =  √[4^2  - 2^2 ] =  √12  units^2 =  2√3  cm

 

And the area  of triangle ABC  =  1/2 the product of the leg lengths  =

1/2 * AC * BC  =  1/2 (2√3) ( 2)  =   2√3 cm^2   (1) 

 

And the area  of the circle  = pi  * (diameter /2)^2 = pi * (4/2)^2  = pi * 2^2  = 4 pi cm^2  (2)

 

So....the shaded area  =

 

area of the circle - area of triangle ABC  =

 

(2)  - (1)  =

 

[ 4pi - 2√3 ) cm^2   ≈     9.10  cm^2

 

 

cool cool cool

 Jun 27, 2018

15 Online Users

avatar