Final answer:
The area of a decagon with a side length of 3.25 m and an apothem of 5m is calculated using the formula for a regular polygon's area, which is half the product of its perimeter and apothem. The correct calculation yields an area of 81.25 m², which does not match any of the given options, suggesting a potential error in the provided information.
Step-by-step explanation:
To find the area of a decagon with a side length of 3.25 m and an apothem of 5m, we can use the formula for the area of a regular polygon: Area = (1/2) × Perimeter × Apothem. First, we need to find the perimeter of the decagon. Since a decagon has 10 sides, the perimeter (P) is 10 times the length of one side. So, P = 10 × 3.25 m = 32.5 m.
Next, we use the previously mentioned formula to calculate the area: Area = (1/2) × 32.5 m × 5 m = 81.25 m², which is not one of the provided options. Since none of the options match the calculated area, there might be a mistake in the options given or in the provided measurements. Always cross-check provided data and calculations for accuracy.