Question

the base of a hexagonal prism has an apothem measuring 10 inches and an area of 346.41 square inches. the prism is 12 inches tall. what is the approximate lateral area of the prism? round to the nearest whole number. 139 square inches 416 square inches 693 square inches 831 square inches

Explanation:

Step1: Find base side length

First, use the regular polygon area formula $A = \frac{1}{2} \times a \times P$, where $A=346.41$, $a=10$. Rearrange to find perimeter $P$:
$$P = \frac{2A}{a} = \frac{2 \times 346.41}{10} = 69.282$$
For a hexagon, $P=6s$, so side length $s = \frac{P}{6} = \frac{69.282}{6} = 11.547$

Step2: Calculate lateral area

Lateral area of prism: $L = P \times h$, where $h=12$
$$L = 69.282 \times 12 = 831.384$$

Step3: Round to whole number

Round 831.384 to nearest integer: $831$

Answer:

831 square inches