+0  
 
+5
113
2
avatar

Let A, B, C, be three points on a line such that AB = 2 and BC = 4. Semicircles are drawn with diameters AB, AC, and BC. Find the area of the shaded region.

 

Guest Feb 27, 2017
 #2
avatar+87293 
0

The area of the shaded region wiil be the area of the semi-circle with the diameter AC mnus the areas of the two smaller semi-circles with diameters  AB and AC

 

Radius of  large semi-circle with diameter AC  = [AB + BC] / 2  =  [ 2 + 4 ] / 2 = 6/2  = 3

 

And the radiuses of AB and BC  = 1  and 2 , respectively

 

So  the shaded area  =

 

(1/2) pi [ 3^2 - 1^2 - 2^2]  = (1/2)  pi [ 9 - 1 - 4 ]   = (1/2) 4pi units^2  = 2 pi units^2

≈  6.28 units^2

 

 

cool cool cool

CPhill  Feb 27, 2017

13 Online Users

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.