Find the area of the regular polygon. Give the answer to the nearest tenth. A pentagon with a side of 8 m
123.9 m²
61.9 m²
49.5 m²
110.2 m²
The correct answer is 110.2 m².
To find the area of a regular polygon, you can use the formula:
Area = (apothem * perimeter) / 2
In this case, the apothem of a regular pentagon can be calculated using the formula:
Apothem = s / (2 * tan(180°/n))
where s is the side length of the pentagon (8 m) and n is the number of sides (5 for a pentagon).
Calculating the apothem:
Apothem = 8 / (2 * tan(180°/5))
Apothem = 8 / (2 * tan(36°))
Apothem = 8 / (2 * 0.7265)
Apothem = 8 / 1.453
Apothem ≈ 5.504 m
Then, you can calculate the perimeter of the pentagon:
Perimeter = 5s
Perimeter = 5 * 8
Perimeter = 40 m
Finally, plug in the values to the area formula:
Area = (5.504 * 40) / 2
Area = 220.16 / 2
Area = 110.08 m²
Rounded to the nearest tenth, the area is 110.2 m².