Answered

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HELPP PLEASE

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?
Round to the nearest tenth of a millimeter.

Sagot :

raphealnwobi

Answer:

27.5 mm

Step-by-step explanation:

The game piece has the shape of two identical square pyramids attached at their bases. Given that the perimeters of the square bases are 80 millimeters, and the slant height of each pyramid is 17 millimeters.

Let the side length of each of the side of the base of the pyramid be b, hence:

perimeter = 4b

80 = 4b

b = 20 mm. half of the side length = b/2 = 20 / 2 = 10 mm

The slant height (l) = 17 mm, Let h be the height of one of the pyramid, hence, using Pythagoras theorem:

(b/2)² + h² = l²

17² = 10² + h²

h² = 17² - 10² = 189

h = √189

h = 13.75 mm

The length of the game piece = 2 * h = 2 * 13.75 = 27.5 mm.

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