Praxis Core Academic Skills for Educators: Mathematics (5733)GeometryHard
A designer is creating a custom-shaped swimming pool. The pool's base can be modeled as a composite figure consisting of a rectangle and a semicircle. The rectangle is 10 meters long and 6 meters wide. The semicircle is attached to one of the 6-meter sides. What is the approximate total area of the pool's base?
- A88.27 m²
- B74.13 m²
- C113.10 m²
- D69.42 m²
Show answer & explanationAnswer & explanation
Correct answer: B. 74.13 m²
The total area is the sum of the area of the rectangle and the area of the semicircle. Area of rectangle = length × width = 10 m × 6 m = 60 m². The diameter of the semicircle is equal to the width of the rectangle, so d = 6 m, which means the radius r = 3 m. Area of semicircle = (1/2) * πr² = (1/2) * π * (3)² = (1/2) * π * 9 = 4.5π. Using π ≈ 3.14159, Area of semicircle ≈ 4.5 * 3.14159 ≈ 14.137 m². Total area = Area of rectangle + Area of semicircle = 60 m² + 14.137 m² ≈ 74.137 m², approximately 74.13 m².
Why the other options are wrong
- A. Incorrect. This is approximately 60 + 9π, possibly from not dividing by 2 for the semicircle.
- C. Incorrect. This is approximately the area of a circle with radius 6m, or 36π.
- D. Incorrect. This might result from using radius 6, or incorrect calculation of semicircle area.
Area of Composite Figures
The total area of a two-dimensional shape made up of two or more simpler geometric shapes.
- Break down the complex figure into simpler, recognizable shapes (e.g., rectangles, triangles, circles).
- Calculate the area of each individual simpler shape.
- Add or subtract the areas as appropriate to find the total area of the composite figure.
Memory trick: Divide and conquer: Break it down, calculate parts, then add it up.