Question

find the lateral area of the prism. the base is a regular hexagon.
4 ft.
12 ft.
square feet
submit

Explanation:

Step1: Recall lateral area formula for prism

The lateral area \( LA \) of a prism is given by \( LA = \text{Perimeter of base} \times \text{height (or length) of the prism} \). For a regular hexagon base, each side length \( s = 4 \) ft. A regular hexagon has 6 sides, so the perimeter \( P \) of the base is \( P = 6 \times s \).

Step2: Calculate the perimeter of the base

Substitute \( s = 4 \) ft into the perimeter formula: \( P = 6 \times 4 = 24 \) ft.

Step3: Calculate the lateral area

The length of the prism (the distance between the two hexagonal bases) is \( l = 12 \) ft. Using the lateral area formula \( LA = P \times l \), substitute \( P = 24 \) ft and \( l = 12 \) ft: \( LA = 24 \times 12 \).

Step4: Compute the product

\( 24 \times 12 = 288 \).

Answer:

288