Answer to Question #272014 in Trigonometry for jam

Question

The lateral edge of a pyramidal church spire is 61 ft. Each side of the

octagonal base is 22 ft. What will be the cost of painting the spire at

$0.025 a square foot?

Answer 1

$\text{First, we calculate the total surface area of the octagon, where }\\ \text{Total surface area = Lateral surface area + base surface area}\\ \text{The base surface area is given by}\\ 2(1+\sqrt{2})a^2=2(1+\sqrt{2})22^2\\ = 2336.96\\ \text{The perimeter of the base is given by $22\cdot8=176$} \text{The lateral surface area is given by}\\ \frac12 \cdot 176 \cdot 61 = 5368\\ \text{Hence, the total surface area is }\\ 5368 +2336.96= 7704.96sq. feet\\ \text{the cost of painting is }\\ 7704.96 \cdot 0.025=\$192.624$