Question

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​

Answer 1

perimeter = 14.28

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

Answer 2

First, find the circumference of the circle and divide it by 4. Then add lines AB and BC to that (these two lines are both radiuses of the circle).

P = πd/4 + 4 + 4
= π(8)/4 + 4 + 4
= 25.12/4 + 4 + 4
= 6.28 + 4 + 4
= 14.28

Therefore, the perimeter of the shaded region is 14.28.