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Find the area and the perimeter of the shaded regions below. 

 

 Aug 4, 2020
 #1
avatar+28021 
+1

TWO triangle hypotenuses      find via pythag theorem

    h^2 = 4^2 + 10^2        solve for h    rememeber: there are 2

 

semicircle perimeter =   1/2  pi d   = 1/2 pi * 8         add them together

 Aug 4, 2020
 #2
avatar+1154 
+1

AREA:   10*8/2 for the area of the triangle and π4^2 so we add them up in a equation to get that the area 80/2+π4^2=40+16π so the area of the shaded region is 40+16π or \(\boxed{40+16π}\)

 

Circumfrence=8π/2 for the rounded part and 2*(sqrt(10^2+(8/2)^2)) again we make them into an equation 4π+2*(sqrt(10^2+4^2))=4π+2*(sqrt(116)) then we simplify it to get 4π+4*(sqrt(29)) or \(4π+4\sqrt{29}\)

 Aug 4, 2020

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