Find the area of the regular polygon. Give the answer to the nearest tenth. A pentagon with a side of 8 m (1 point) Responses 123.9 m2 123.9 m2 49.5 m2 49.5 m2 110.2 m2 110.2 m2 61.9 m2
To find the area of a regular polygon, we can use the formula:
Area = (perimeter * apothem) / 2
In this case, the perimeter of the pentagon (a regular polygon with 5 sides) is 5 * 8 = 40 m.
To find the apothem, we can divide the side length by 2 * tan(180° / n), where n is the number of sides of the polygon (in this case, 5).
apothem = 8 / (2 * tan(180° / 5))
= 8 / (2 * tan(36°))
= 8 / (2 * 0.726)
≈ 5.5 m
Now, we can plug the values into the formula to find the area:
Area = (40 * 5.5) / 2
= 220 / 2
= 110 m^2
Therefore, the area of the pentagon is approximately 110.2 m^2 to the nearest tenth.
So, the answer is: 110.2 m^2.