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Listen Find the area of a pentagon with an apothem of 5 units. Round your answer to the nearest hundredth. A~~ ◻ square units

Listen\newlineFind the area of a pentagon with an apothem of 55 units. Round your answer to the nearest hundredth.\newlineA≈ A \approx □ \square square units

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Full solution

Q. Listen\newlineFind the area of a pentagon with an apothem of 55 units. Round your answer to the nearest hundredth.\newlineA≈ A \approx □ \square square units
  1. Identify Formula: Step 11: Identify the formula to calculate the area of a regular pentagon, which is (52)×Perimeter×Apothem(\frac{5}{2}) \times \text{Perimeter} \times \text{Apothem}.
  2. Find Perimeter: Step 22: We need the perimeter, but it's not given. Assume each side of the pentagon is equal, let's say each side is ' extit{s}'. The perimeter ( extit{P}) of the pentagon is 5s5s.
  3. Calculate Area: Step 33: Substitute the values into the area formula. Area=(52)×5s×5\text{Area} = \left(\frac{5}{2}\right) \times 5s \times 5. Simplify it to get Area=62.5s\text{Area} = 62.5s.

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