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Geometry/Octagonal Pyramid Surface Area

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Question
A playhouse is in the shape of a regular octagonal pyramid with a side length of 3 feet and a slant height of 12 feet.  The wood used to build the walls cost $3 per square foot. What is the cost of the wood for the walls of the playhouse?   Surface area for octagonal pyramid  (???)  4 (length)(slant height) + length (square)

 4(12)(3)  + (3) square
 4(36)  + 9
  144  + 9  =  153      153($3.00) = $459.00

Answer
Hi Gina,

The total surface area of any pyramid is the sum of the base area and the lateral area.  The lateral area is made up entirely of triangles.  If you want the wood for the walls of the playhouse, you are only concerned with the area of those 8 triangles.  Each triangle has area (length)(slant height)/2.  You are close to the correct answer, but there is no need to add the "length squared" term.

Thanks for asking,
Azeem

Geometry

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Azeem Hussain

Expertise

I welcome your questions on algebra, 2D and 3D geometry, parabolic functions and conic sections, and any other mathematical queries you may have.

Experience

4 years as a drop-in and by-appointment tutor at Champlain College. Private tutor for dozens of clients over the past 8 years.

Publications
CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry

Education/Credentials
Bachelor of Science, Major Mathematics and Major Economics, McGill University, 2014. Diploma of Collegiate Studies; Pure and Applied Science, Champlain College Saint-Lambert, 2010.

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