Question

An eight-sided game piece is shaped like

Answer 1

Answer:

27.5 mm

Step-by-step 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.