GED Mathematical Reasoning TestQuantitative Problem Solving with MeasurementHard
A packaging company is designing a new gift box in the shape of a square pyramid. The base of the pyramid is a square with side lengths of 6 inches, and the slant height of each triangular face is 5 inches. What is the total surface area of the pyramid, including the base?
- A36 in²
- B60 in²
- C96 in²
- D120 in²
Show answer & explanationAnswer & explanation
Correct answer: C. 96 in²
The total surface area of a square pyramid is the area of its square base plus the area of its four triangular faces. Calculate the base area (side²) and the area of one triangular face (0.5 × base × slant height), then multiply the triangular area by 4 and add to the base area.
Why the other options are wrong
- A. This is only the area of the base (6*6).
- B. This is only the lateral surface area (4 * 0.5 * 6 * 5).
- D. This is an overestimation, likely from an arithmetic error.
Surface Area of a Square Pyramid
The sum of the area of the square base and the areas of all four triangular lateral faces.
- Formula: Base Area + Lateral Area
- Base Area = side²
- Lateral Area = 4 × (0.5 × base side × slant height)
Memory trick: Base Plus Four Triangles for Pyramid's Skin