SOLUTION: I'm trying to find the surface area of a regular pyramid. The base is a square, it's side lengths are 5ft, and the slant height is 6ft. How do I find the apothem so I can complete

Algebra ->  Surface-area -> SOLUTION: I'm trying to find the surface area of a regular pyramid. The base is a square, it's side lengths are 5ft, and the slant height is 6ft. How do I find the apothem so I can complete       Log On


   

Question 624374: I'm trying to find the surface area of a regular pyramid. The base is a square, it's side lengths are 5ft, and the slant height is 6ft. How do I find the apothem so I can complete the equation SA=LA+1/2(A)(P)
I did the lateral area calculations with the formula LA=1/2(P)(H)
LA=0.5(25)(6), but now I need to know how to get the apothem in order to find the surface area. Please explain it. Thank you.
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
the pyramid has a square base.
your dimensions are:
length of base is equal to 5 feet.
slant height is equal to 6 feet.
you want to find the surface area.
the slant height of the pyramid is the apothem which is the height of each triangular face.
you have all the information you need.
the area of the base is 5*5 = 25 square feet.
the area of one of the triangular faces of the pyramid is equal to 1/2 * 5 * 6 = 15.
multiply that by 4 and you get a total of 60 square feet for the triangular faces.
add all those together and you get a total surface area of 60 + 25 = 85 square feet.
a reference can be found here:
http://mathworld.wolfram.com/SlantHeight.html