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# stuck on this

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An eight-sided game piece is shaped like two identical square pyramids attached at their bases. The perimeters of the square bases are 80 millimeters, and the slant height of each pyramid is 17 millimeters. What is the length of the game piece?

Feb 19, 2020

#1
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If the perimeter  of a square base  = 80 mm, then the side of one of these squares  = 20mm

The length of the diagonal of the square  =  √2 * side length   = √2 * 20  =  20√2 mm

And (1/2)  of this length  is the leg of a right triangle with the slant height the  hypotenuse =  10√2  =  √200 mm

Using the Pythagorean Theorem...(1/2)  the height of this game piece  =

√ [slant height^2  - (1/2 diagonal length)^2]   =

√[17^2 - (√200)^2  ]  =   √[289 - 200 ]  = √89  mm

So....the height of the game piece is  twice this   =  2√89 mm ≈  18.87 mm

Feb 19, 2020
#3
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Hi CPhill ! Your answer differs from mine, and I can see why.

You've calculated the height using square's diagonal instead a side of it.

Dragan  Feb 19, 2020
#2
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An eight-sided game piece is shaped like two identical square pyramids attached at their bases. The perimeters of the square bases are 80 millimeters, and the slant height of each pyramid is 17 millimeters. What is the length of the game piece?

Square side is        a = 80/4 = 20 mm      a/2 = 10 mm

Slant height is         S = 17 mm

Pyramid height        h = sqrt [S2 - ( a/2 )2]     h = 13.74772708 mm

The length of the game piece is      L = 2h = 27.49545417 mm

Feb 19, 2020
edited by Dragan  Feb 19, 2020
edited by Dragan  Feb 19, 2020