SOLUTION: 1. find the area of the portion of the semi circle shown in the figure which is outside of the inscribed triangle. the figure has a triangle scalene and AC= 16 and CB=10.

Question 827493: 1. find the area of the portion of the semi circle shown in the figure which is outside of the inscribed triangle. the figure has a triangle scalene and AC= 16 and CB=10.
Answer by Edwin McCravy(20055) (Show Source): You can put this solution on YOUR website!



An angle inscribed in a semicircle is always a right angle.
Therefore ΔABC is a right triangle, and we can take its two legs
as its base and height.

So the area of ΔABC =  =  = 80

Since ΔABR is a right triangle, we can find the hypotenuse AB using
the Pythagorean theorem:

AB�=AC�+CB�
AB�=16�+10�
AB�=256+100
AB�=356
 AB= =  = 

AB is the diameter of the semicircle.  Since the radius is
half the diameter, the radius is .

Area of a whole circle is  so 
Area of a semicircle = 

So the area of this semicircle is 

 =  = 139.8008731

So the area of the portion of the semicircle which is outside of the 
inscribed right triangle ΔABC is 

area of semicircle - area of triangle =

139.8008731 - 80 = 59.80087308

Edwin

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