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# Find the perimeter of the semicircular region. Round to the nearest hundredth. # Find the perimeter of the semicircular region. Round to the nearest hundredth.

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Circles asked 2021-01-15
Find the perimeter of the semicircular region. Round to the nearest hundredth.

## Answers (1) 2021-01-16
The perimeter of a semicircle region is the curved distance around the semicircle plus the diameter of the semicircle.
The curved distance around the semicircle is half of the circumference of the full circle. The formula for circumference is C=πd where d is the diameter. Half of the circumference would then be $$\displaystyle\frac{{1}}{{2}}π{d}$$. Since the diameter of the semicircle is 9 m, you need to substitute d=9 into $$\displaystyle\frac{{1}}{{2}}π{d}$$. This gives $$\displaystyle\frac{{1}}{{2}}π{\left({9}\right)}={4.5}π{m}.$$
The diameter of the semicircle is 9 m so the perimeter is then curved distance + diameter = $$\displaystyle{4.5}π+{94.5}π+{9}.$$ Using a calculator to evaluate gives $$\displaystyle{4.5}π+{9}≈{23.14}.$$ The perimeter of the semicircle is then about 23.14 m.

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