FTCE Professional Education Practice Exam

What is the formula for the lateral area of a pyramid?

1. 1/2PI

2. 1/3Bh

3. B + 1/2PI

4. 3.14(r^2)(h)

The correct answer is: 1/2PI

The formula for the lateral area of a pyramid is not accurately described by option A. The correct answer involves calculating the lateral area based on the perimeter of the base and the slant height of the pyramid. The lateral area of a pyramid is calculated using the formula: \[ \text{Lateral Area} = \frac{1}{2} \times \text{Perimeter of the base} \times \text{Slant height} \] This formula highlights that the lateral area depends on the perimeter of the base, as it accounts for all the triangular faces of the pyramid that connect the base to the apex. The other options capture different geometric concepts but do not pertain to the lateral area of a pyramid. For example, option B represents the volume of a pyramid, defined by the formula \( V = \frac{1}{3}Bh \), where B is the area of the base and h is the height. Overall, understanding the geometric properties of a pyramid, including its base and triangular faces, is key to deriving the correct formula for the lateral area.