SOLUTION: Hi, my class just started studying pyramids and I need help on a problem. I'm really terrible at geometry and we don't take notes in our class and would really appreciate some help

Algebra ->  Surface-area -> SOLUTION: Hi, my class just started studying pyramids and I need help on a problem. I'm really terrible at geometry and we don't take notes in our class and would really appreciate some help      Log On


   

Question 193071This question is from textbook Geometry Connections
: Hi, my class just started studying pyramids and I need help on a problem. I'm really terrible at geometry and we don't take notes in our class and would really appreciate some help! This is how the problem is worded exactly in my book: "The TransAmerica building in San Francisco is built of concrete and is shaped like a square-based pyramid. The building is periodically power-washed using one gallon of cleaning solution for every 250 square meters of surface, As the new building manager, you need to order the cleaning supplies for this large task. The problem is that you do not know the height of each triangular face of the building; you only know the vertical height of the building from the base to the top vertex."
"Your Task: Determine the amount of cleaning solution needed to wash the TransAmerica building if an edge of the square base is 96 meters and the height of the building is 220 meters. Include a sketch in your solution."
I have the answers from another website, but it doesn't show how to get them. I've tried to get the solutions, but have no idea what process I must got through. The answers are as follows:
Surface Area≈43,234 square meters. This does not include the area of the base, which is 9, 216 square meters. Therefore, ≈173 gallons of cleaning solution are needed. This question is from textbook Geometry Connections

Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
You'll need to find the lateral surface area (S) (that's the area of the four triangular faces)of the pyramid. This is given by:
S = 1/2(Perimeter of the base)X(the slant height)
So you'll need the slant height of the pyramid.
To find the slant height, drop a perpendicular line from the vertex (apex) of the pyramid to the base. Now draw a line from where this intersects the base, perpendicular to one edge of the base.
You now have a right triangle whose height (220m) is that of the pyramid and whose base (half of 96m) is the line from the center to the edge of the base, and whose hypotenuse is the slant height (sl) of the pyramid.
Using the Pythagorean theorem, find the length of the hypotenuse (slant height of the pyramid) of this right triangle.
%28sl%29%5E2+=+220%5E2%2B48%5E2
%28sl%29%5E2+=+48400%2B2304
%28sl%29%5E2+=+50704 Take the square root of both sides.
sl+=+225.175m. This is the slant height.
Now you can calculate the lateral surface area of the pyramid:
S+=+%281%2F2%29%284%29%2896%29%28225.175%29
S+=+%281%2F2%29%28384%29%28225.175%29
S+=+43233.6 Round to the nearest sq.meter.
S+=+43234sq.meters. Now divide this by 250 sq.meters/gallon of cleaning fluid to get:
43234/250 = 172.936 gallons.
So, you'll need 173 gallons of cleaning fluid.