Question

question 10
1 pts
an aboveground swimming pool is 2.75 meters high. the base is a regular octagon whose sides are each 2.20 meters long. compute the lateral area of the pool
48.4 sq m
4 sq m
48.4 m
17.6 m

Explanation:

Step1: Recall lateral area formula for prism

A regular octagonal prism (the pool) has lateral area \( L = Ph \), where \( P \) is the perimeter of the base, \( h \) is the height.

Step2: Calculate perimeter of octagonal base

A regular octagon has 8 equal sides. Each side \( s = 2.20 \, \text{m} \), so perimeter \( P = 8s = 8\times2.20 = 17.6 \, \text{m} \).

Step3: Calculate lateral area

Height \( h = 2.75 \, \text{m} \), so \( L = Ph = 17.6\times2.75 \).
\( 17.6\times2.75 = (17 + 0.6)\times2.75 = 17\times2.75 + 0.6\times2.75 = 46.75 + 1.65 = 48.4 \, \text{sq m} \).

Answer:

48.4 sq m