Question

find the lateral area of the prism. the base is a square. 12 ft. 6 ft. 6 ft.

Explanation:

Step1: Recall lateral area formula for prism

The lateral area \( LA \) of a prism is given by the perimeter of the base \( P \) multiplied by the height \( h \), i.e., \( LA = P \times h \).

Step2: Find perimeter of square base

The base is a square with side length \( s = 6 \) ft. The perimeter of a square is \( P = 4s \). Substituting \( s = 6 \), we get \( P = 4 \times 6 = 24 \) ft.

Step3: Identify height of prism

The height \( h \) of the prism is 12 ft (from the diagram).

Step4: Calculate lateral area

Using the formula \( LA = P \times h \), substitute \( P = 24 \) ft and \( h = 12 \) ft. So, \( LA = 24 \times 12 = 288 \) square feet.

Answer:

The lateral area of the prism is \(\boldsymbol{288}\) square feet.