Question

find the lateral area of the prism. the base is a regular penta
12 yd.
20 yd.
square yards
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Explanation:

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

The lateral area \( LA \) of a prism is given by the formula \( LA = P \times h \), where \( P \) is the perimeter of the base and \( h \) is the height (or length) of the prism.

Step2: Determine the perimeter of the regular pentagonal base

A regular pentagon has 5 equal sides. From the diagram, each side of the pentagonal base is 12 yards. So the perimeter \( P \) of the regular pentagon is \( P = 5 \times \text{side length} \). Substituting the side length (12 yd), we get \( P = 5 \times 12 = 60 \) yards.

Step3: Identify the height of the prism

The height \( h \) of the prism (the distance between the two pentagonal bases) is given as 20 yards.

Step4: Calculate the lateral area

Using the formula \( LA = P \times h \), substitute \( P = 60 \) yd and \( h = 20 \) yd. So \( LA = 60 \times 20 = 1200 \) square yards.

Answer:

1200