Question 199256
Remember  that  a  triangle  inscribed  in a  semicircle  is  a  rt  triangle,,,,therefore  we  have  a  rt  isosceles  triangle ,,,with  hypotenuse  = 32. 
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since  the  ratio  of  sides  are  1 :1:sqrt2 ,,,,  32 / sqrt2  = s / 1,,, or  s= 22.627,,,(16 sqrt2)
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Area  of  triangle  =  1/2  *b *h =  1/2 * 22.627 *22.627 = 256
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Area  of  semi  circle  = 1/2  * pi * r^2 = 1/2 * pi * 16^2 = 128 * pi
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Area  of  shaded  area  between  is  ( 128 pi - 256) = 128 (pi-2)