SOLUTION: Find the area and perimeter of the shaded region. <a href="http://tinypic.com" target="_blank"><img src="http://i27.tinypic.com/2edxqjd.jpg" border="0" alt="Image and video hostin

Algebra ->  Circles -> SOLUTION: Find the area and perimeter of the shaded region. <a href="http://tinypic.com" target="_blank"><img src="http://i27.tinypic.com/2edxqjd.jpg" border="0" alt="Image and video hostin      Log On


   

Question 134188: Find the area and perimeter of the shaded region.
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note: The radius of the circle is 4.
What I've done:
I know you have to find the area of the small unshaded seg. by doing A seg. = Asec.-A triangle. Then you need to find the area of the semi-circle created by the shaded area and the segment. Then if you subtract the area of the segment from the area of the semi-circle you get the area of the shaded region. I just don't get how to find the area of the semi circle and I don't know what to input into the formula for finding the area of the SEGMENT.
I also have no clue how to find the perimeter of the shaded area!
PLEASE HELP!


Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
the diameter of the semicircle is the hypotenuse of the triangle

the segment area is 1/4 the area of the circle minus the area of the triangle
__ the central angle is 90°

the perimeter of the shaded area is the length of the outer side (which is the circumference of the semi-circle)
__ plus the length of the inner side (which is 1/4 the circumference of the large circle)