Question

find the lateral area of the prism. the base is a square. 14 m 7 m 7 m

Explanation:

Step1: Recall the formula for the lateral area of a prism

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

Step2: Calculate the perimeter of the square base

The base is a square with side length \( s = 7 \, \text{m} \). The perimeter \( P \) of a square is \( 4 \times s \). So, \( P = 4 \times 7 = 28 \, \text{m} \).

Step3: Identify the height of the prism

From the diagram, the height \( h \) of the prism is \( 14 \, \text{m} \).

Step4: Calculate the lateral area

Using the formula \( LA = P \times h \), substitute \( P = 28 \, \text{m} \) and \( h = 14 \, \text{m} \). So, \( LA = 28 \times 14 = 392 \, \text{m}^2 \).

Answer:

The lateral area of the prism is \( 392 \, \text{square meters} \) (or \( 392 \, \text{m}^2 \)).