Question

The Palace of Peace and Accord in Astana, Kazakhstan, was built in 2006. The building has a square right pyramid structure. The length of a side of the square base is 62 m, start text, m, end text, and the vertical height of the pyramid is also 62 m, What is the height of one of the triangular faces? Round your answer to the nearest tenth.

Answer 1

69.3m

Explanation:

-Given the base side length is 62m and the vertical height is 62m.

-The vertical height touches the square base at its midpoint. We therefore use half the base length and the height to calculate the slant heights.

#Using Pythagorean theorem:

`b^2+h^2=H^2, h=62, b=0.5* 62=31\\\\H^2=62^2+31^2\\\\H=4805^{(1)/(2)}\\\\=69.32\approx69.3 \ m`

Hence, the heights of the triangular faces is 69.3m