SOLUTION: The pyramid in the diagram below has a square base, 40 feet on each side. Its slant height is 160 feet. What is the surface area of the pyramid?

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Question 753552: The pyramid in the diagram below has a square base, 40 feet on each side. Its slant height is 160 feet. What is the surface area of the pyramid?
Answer by malglu(63) (Show Source):
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The pyramid in the diagram below has a square base, 40 feet on each side. Its slant height is 160 feet. What is the surface area of the pyramid?
first you need the area of the base, which is 40foot * 40 foot. then you need to add this to 4 * the surface area of one of the sides. these sides are triangler in shape. the base is 40 foot and the two slanting sides are 160 feet. the area of a traingle is 1/2 * base * perpendicular height. use pythagurus's theorem to calculate the perpendicular height. 160 ^2 = 40 ^2 + x^2 (the perpendicular height)
25600 - 1600 = x^2
24000 = x^2
take roots of each side
x = 154.99 to 2 dp
now 1/2 * base (40) * 154.99 = 3098.39 to 2 dp
* 4 = 12393.55
+ 1600 (area of base) = 13993.55 squared feet to 2 dp