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Eddi Din [679]
3 years ago
13

Find the area of a regular pentagon with an apothem of 11 units. *

Mathematics
1 answer:
docker41 [41]3 years ago
3 0

Answer:

<h2>440 square units</h2>

Step-by-step explanation:

We can find half of a side of the pentagon with the expression

tan(36\°)=\frac{s_{half} }{11}

Because, as a regular polygon, all its sectors have the same central angle, and the apothem divides equally each sector in two equal parts.

s_{half} \approx 8

Therefore, half of a side is 8 units long, which means each side measures 16 units.

Now, the area of a penthagon is defined by

A=\frac{p \times a}{2}

Where p is the perimeter and a is the apothem. Where the perimeter is the sum of all sides, which is 80 units.

A= \frac{80 \times 11}{2} =440 \ u^{2}

Therefore, the right answer is the second choice.

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