Question

a square pyramid has a base with side lengths each measuring 40 inches. the pyramid is 21 inches tall, with a slant height of 29 inches. what is the surface area of the pyramid? 3,280 inches 3,280 square inches 3,920 inches 3,920 square inches

Explanation:

Step1: Calculate base - area

The base is a square with side length $s = 40$ inches. The area of the base $B$ is given by $B=s^{2}$. So, $B = 40^{2}=1600$ square inches.

Step2: Calculate area of one triangular face

The formula for the area of a triangle is $A=\frac{1}{2}bh$, where $b$ is the base and $h$ is the height. For the triangular faces of the square - pyramid, $b = 40$ inches (base of the triangle is the side of the square base) and $h = 29$ inches (slant height). So, the area of one triangular face $A_{t}=\frac{1}{2}\times40\times29 = 580$ square inches.

Step3: Calculate total area of four triangular faces

Since there are 4 triangular faces, the total area of the triangular faces $A_{total - t}=4\times A_{t}=4\times580 = 2320$ square inches.

Step4: Calculate surface area of the pyramid

The surface area $SA$ of a square - pyramid is the sum of the base area and the total area of the triangular faces. So, $SA=B + A_{total - t}=1600+2320=3920$ square inches.

Answer:

D. 3,920 square inches