Praxis Core Academic Skills for Educators: Mathematics (5733)GeometryHard
A city planner is evaluating the area of a proposed park, which is shaped like a regular pentagon. If the length of one side of the pentagon is 80 meters, and its apothem (distance from center to midpoint of a side) is approximately 55.05 meters, what is the approximate area of the park?
- A44040 m²
- B22020 m²
- C8808 m²
- D11010 m²
Show answer & explanationAnswer & explanation
Correct answer: D. 11010 m²
The area of a regular polygon can be calculated using the formula A = (1/2) * P * a, where P is the perimeter and a is the apothem. For a regular pentagon with side length s = 80 meters, the perimeter P = 5 * s = 5 * 80 = 400 meters. Given the apothem a ≈ 55.05 meters. Area A = (1/2) * 400 * 55.05 = 200 * 55.05 = 11010 m².
Why the other options are wrong
- A. Incorrect. This is 2 * Perimeter * Apothem, or (5*80)*(55.05)*2.
- B. Incorrect. This is Perimeter * Apothem, forgetting to divide by 2.
- C. Incorrect. This might be from using (1/2) * 4 * 55.05 * 80 or other miscalculation.
Area of a Regular Polygon (using Apothem)
The area of a polygon with all sides and all angles equal, calculated using its perimeter and apothem.
- Formula: A = (1/2) * P * a, where P is the perimeter and a is the apothem.
- The apothem is the distance from the center to the midpoint of any side, perpendicular to that side.
- Perimeter P = n * s, where n is the number of sides and s is the side length.
Memory trick: Perimeter times Apothem, then 'Half' it for the area.