The length of a diameter of the circle shown is 8.if angle abc is a right angle, what is the perimeter of the shaded region

perimeter = 14.28

Step-by-step explanation:

Since a diameter of the circle has length 8, then a radius has length 8/2 = 4.

We have r = 4.

For a circle of radius, r, circumference = 2(pi)r.

The shaded area is a quarter circle.

Its perimeter is the length of 2 radii plus the length of a quarter circumference of the circle.

perimeter = radius (segment AB) + radius (segment BC) + arc length (arc AC)

perimeter = r + r + (1/4)(2)(pi)r

perimeter = 4 + 4 + 0.5 * pi * 4

perimeter = 14.28

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