If a 4 minutes 1 of the area that a one is
If a 4 minutes 1 of the area of a circle is
In the number above, circle C has a radius the 18, and the measure of edge ACB is equal to 100°. What is the perimeter the the red shaded region?
The perimeter of any an ar is the full distance approximately its boundaries. The perimeter of the shaded an ar consists of the two straight line segments, AC and also BC, and the arc AB. In stimulate to discover the perimeter of the whole region, we must add the lengths of AC, BC, and the arc AB.
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The lengths of AC and also BC room both going come be same to the length of the radius, i m sorry is 18. Thus, the perimeter of AC and also BC with each other is 36.
Lastly, us must uncover the length of arc AB and add it come 36 to gain the entirety perimeter the the region.
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Angle ACB is a main angle, and also it intercepts arc AB. The size of AB is going to same a certain portion of the circumference. This portion will be equal to the proportion of the measure up of edge ACB to the measure of the full degrees in the circle. There room 360 levels in any circle. The ratio of the edge ACB to 360 degrees will be 100/360 = 5/18. Thus, the length of the arc AB will be 5/18 of the one of the circle, which equates to 2πr, according to the formula because that circumference.