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# Pyramid

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ABCDE is a right square pyramid.  Find the total surface area of the pyramid.  Find the volume of the pyramid.

May 2, 2022

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First, find the slant height   = sqrt [ 20^2 - 3^2 ] =    sqrt [ 391]

So   the area of  one triangle   = (1/2)(6)sqrt [391]  =  3sqrt [391]

So  the surface  area  = 4 * 3sqrt [391]  + surface area of the base  =

12sqrt [391] + 6^2  =     12 sqrt [ 391 ] + 36  =   12 [ sqrt (391) + 3 ] units^2

To find the volume  find the height

The diagonal across the base =  6sqrt 2

So (1/2)  of this =  3sqrt (2) =  sqrt (18)

So the height  =   sqrt [ 20^2 - (sqrt 18)^2 ]  =  sqrt  (382)

So the volume =  (1/3) area of base * height  =

(1/3) 6^2 * sqrt (382)  =

12 sqrt (382)  units^3

May 2, 2022
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Guest May 2, 2022
#4
+124698
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Sorry....I didn't see anyone typing.....!!!

CPhill  May 2, 2022
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I think this website only displays when users are typing, not guests.

Guest May 2, 2022
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I hope this is correct.

Surface Area: 6*6 = 36 for base. sqrt(391) is the distance from the midpoint of a side to the top of the pyramid, due to Pythagorean Theorem. 3sqrt(391) is the area of one of the sides. The answer after we multiply that by four and add 36 is 12sqrt(391) + 36.

Volume: The volume of a pyramid is the area of the base times the height, divided by 3. the base is 6*6 = 36. Since the distance from the midpoint of a side to the top of the pyramid is sqrt(391), and the distance from that to the center of the pyramid is 3, we use the Pythagorean Theorem. We find that the height of the pyramid is sqrt(382). Our answer is 12sqrt(382).

May 2, 2022