Question

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.

Answer 1

27.5 mm

Explanation:

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

perimeter of square = 4a

80 = 4a

a = 20 mm.

The distance from the middle of the square pyramid to the side = r = half of the side length = a/2 = 20 / 2 = 10 mm.

r = 10 mm

The slant height (s) = 17 mm, Let h be the height of each of the pyramid. Using Pythagoras theorem:

r² + h² = s²

17² = 10² + h²

h² = 17² - 10² = 189

h = √189

h = 13.748 mm

The length of the game piece = 2 * h = 2 * 13.748 = 27.5 mm to nearest tenth of a mm.