Question

a square pyramid has side lengths each measuring 8 centimeters. the height of the pyramid is 3 centimeters. what is the lateral area of the pyramid? 20 square centimeters 64 square centimeters 80 square centimeters 84 square centimeters

Explanation:

Step1: Find the slant height.

Use the Pythagorean theorem. The base of the right - triangle for finding the slant height is half of the side length of the base of the pyramid. The side length of the base $s = 8$ cm, so the base of the right - triangle $a=\frac{s}{2}=4$ cm, and the height of the pyramid $h = 3$ cm. The slant height $l=\sqrt{h^{2}+a^{2}}=\sqrt{3^{2}+4^{2}}=\sqrt{9 + 16}=\sqrt{25}=5$ cm.

Step2: Calculate the lateral area.

The lateral area of a square pyramid $L = 2sl$, where $s$ is the side length of the base and $l$ is the slant height. Substitute $s = 8$ cm and $l = 5$ cm into the formula: $L=2\times8\times5=80$ square centimeters.

Answer:

C. 80 square centimeters