What is the area of a regular pentagon with a side length of 9 millimeters and an apothem length of 6.2 millimeters?

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10-07-2017
Mathematics

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What is the area of a regular pentagon with a side length of 9 millimeters and an apothem length of 6.2 millimeters?

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BlueSky06 BlueSky06 · Answer 1 · 2017-07-24T15:06:51+02:00

The area of a regular polygon is equal to half of the product of its apothem and perimeter.
A = 0.5aP

Find first the perimeter,
P = 5 x (9 mm)
P = 45 mm

Substituting the perimeter and the apothem to the first equation,
A = 0.5(45 mm)(6.2 mm)
A = 139.5 mm²

Therefore, the area of the regular pentagon is equal to 139.5 mm².