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dusya [7]
2 years ago
13

Find the area of the shaded regions. Give your answer as a completely simplified exact value in terms of π (no approximations).

Mathematics
1 answer:
masya89 [10]2 years ago
6 0

Answer:

40\pi \ m^{2}

Step-by-step explanation:

we know that

The area of a circle is equal to

A=\pi r^{2}

In this problem we have

r=10\ m

Substitute and find the area

A=\pi (10)^{2}=100 \pi\ m^{2}

Remember that

360\° subtends the area of complete circle

so

by proportion

Find the area of the shaded regions

The central angle of the shaded regions is equal to 2*72\°=144\°

\frac{100\pi }{360} \frac{m^{2}}{degrees} =\frac{x }{144} \frac{m^{2}}{degrees} \\ \\x=144*100\pi /360\\ \\ x=40\pi \ m^{2}

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