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A region is bounded by semicircular arcs constructed on the side of a square whose sides measure \(2/\pi\), as shown. What is the perimeter of this region?

 Dec 10, 2020

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 #1
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Hi guest, we want to find the perimeter of 4 semicircles and the formula for a circle's perimeter $2(pi)(r)$, since the perimeter is cut in half the formula is $(pi)(r)$.


Now we need to find the radius, since the side of the square and the diameter of the circle are tangent and equal, we know the radius, the formula for radius is $d=2r$.

 

the diameter is 2/pi, therefore making the radius 1/pi, using the formula 1/pi * pi = 1, so the perimeter of 1 semi circle 1, the perimeter of 4 semicircles is:

 

$4$

 Dec 10, 2020
 #1
avatar
+1
Best Answer

Hi guest, we want to find the perimeter of 4 semicircles and the formula for a circle's perimeter $2(pi)(r)$, since the perimeter is cut in half the formula is $(pi)(r)$.


Now we need to find the radius, since the side of the square and the diameter of the circle are tangent and equal, we know the radius, the formula for radius is $d=2r$.

 

the diameter is 2/pi, therefore making the radius 1/pi, using the formula 1/pi * pi = 1, so the perimeter of 1 semi circle 1, the perimeter of 4 semicircles is:

 

$4$

Guest Dec 10, 2020
 #2
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A region is bounded by semicircular arcs constructed on the side of a square whose sides measure 2 / pi, as shown. What is the perimeter of this region?

 

Perimeter      P = 2[ pi(2 / pi)] = 4

 Dec 11, 2020

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