A square pyramid has a base with a perimeter of 40 inches and a height of 12 inches. Find the surface area and volume of the pyramid. Show all work for credit.
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Updated 9/22/2011 3:03:38 PM
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1) to find the surface area of the pyramid, you will need the area of the 4 triangles and the base find the area of the base since the perimeter of the base is 40 each side will be 10 cz [40/4 =10] the area of a square is length x width [ l x w] 10 x 10 = 100 *the area of the base is 100 square inches now, find the area of the 4 triangles this will be quite confusing cz it involve with visualizing a pyramid we know that the height is 12 inches and one side of the base is 10 imagine u are looking through a pyramid, the height will be at the middle [ the center of the base connecting to the sharp corner at the top ] now imagine that there is a triangle inside the square pyramid the height of the triangle is the height of the pyramid, the base of the triangle is half the length of the one side of the base, the hypothuse of the triangle is the slant height of one of the triangles of the pyramid what i just wrote is very confusing, it is hard to understand try to draw it out do u know what is the slant height? ignore the triangle that i wrote about before look back at the pyramid, there are four triangles the slant height will be the height of a triangle but the slant height is the hypothuse for the triangle inside the one that i told u to visualize ALL THat trash that i talk about is very confusing and may not be helpful to u, anyway i will continue to find the surface area of pyramid okay, now we have the area of the base which is 100 square inches we need to find the area of one triangle talking back to the imaginary triangle inside the pyramid find the slant height the height is 12, the base of triangle is 5 cz [the base is half the length of one side of the pyramid which is 10/2] now we find the hypothuse/slant height 12^2 + 5^2= 144 + 25 = 169 square root of 169 = 13 *13 is the slant height looking back at the non-imaginary triangle we know the height of the triangle is 13 and the base is 10 the area of ONE triangle is (13 x 10) / 2 = 65 square inches the area of the FOUR triangles is 65 x 4 = 260 *****the SURFACE area is 260 +100= 360 square inches 2) volume of the pyramid is (1/3)bh base is 10 height is 12 plug in those in the equation (1/3) x 10 x 12 = (1/3) x 120 = 40 *** volume = 40 cubic inches i don't think i helped but i tried =]
stay cool, man.
that is way better than just try. I think you did your best.
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