A playhouse is in the shape of a regular octagonal pyramid with a side length of 3 feet an a slant height of 12 feet. The wood used to build the walls of the playhouse costs $3 per square foot. What is the cost of the wood for the walls of the playhouse?

Question

Cheddar

Mathematics

4 April, 00:22

A playhouse is in the shape of a regular octagonal pyramid with a side length of 3 feet an a slant height of 12 feet. The wood used to build the walls of the playhouse costs $3 per square foot. What is the cost of the wood for the walls of the playhouse?

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Answers (1)

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Swanson · Answer 1

Answer: We just did these problems in my math class today! Ok, so you need to find the lateral surface area, or the area of the faces/walls. The formula for triangles is

1/2 • base • height. Sub in the #s, it would be 1/2 • 6 • 12

1/2•72

36

So now we know the area of one of the faces is 36inches^2, we can multiply that by 4, which is 144. 144•3 ($) = $432. To sum things up, $432 is the cost to build the walls of the playhouse, and we are not adding in the base, because the base is not a face!