Answer :
Final answer:
To find the area of a regular pentagon, we need to know the length of its apothem and the length of its side. The apothem is a line segment drawn from the center of the pentagon to the midpoint of any side, perpendicular to that side. Using the given side length, we can calculate the apothem and then find the area of the pentagon.
Explanation:
To find the area of a regular pentagon, we need to know the length of its apothem and the length of its side.
The apothem is a line segment drawn from the center of the pentagon to the midpoint of any side, perpendicular to that side. The side length of the pentagon is given as 6.2 inches.
Since the pentagon is regular, the apothem is also the radius of the inscribed circle. We can find the apothem using the formula:
apothem = side length / (2 * tan(180° / n)), where n is the number of sides.
For a pentagon, n = 5, so the apothem can be calculated as:
apothem = 6.2 / (2 * tan(180° / 5)) = 6.2 / (2 * tan(36°)).
Using a calculator, we can evaluate the right side of the equation to find the apothem. Once we have the apothem, we can find the area of the pentagon using the formula:
area = (1/2) * apothem * perimeter, where perimeter = 5 * side length.
Plugging in the values: area = (1/2) * (apothem) * (5 * 6.2). Calculate and round the result to the nearest tenth of a square inch.
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