Question

The Palace of Peace and Accord in Astana, Kazakhstan, was built in 20062006. The building has a square right pyramid structure. The length of a side of the square base is 62\,\text{m}62m, and the vertical height of the pyramid is also 62\,\text{m}62m. What is the height, hh, of one of the triangular faces? Round your answer to the nearest tenth.

Answer 1

slant height = 69.3

Answer 2

69.3 meters.

Explanation:

Let h be the height of one of the triangular faces.

We have been given that The Palace of Peace and Accord has a square right pyramid structure. The length of a side of the square base is 62 m, and the vertical height of the pyramid is also 62 m.

We will use Pythagorean theorem to find the height of the triangular face (slant height) of our given square right pyramid.

`\text{Slant height}=\sqrt{\text{Height}^2+\text{Half the base length}^2}`

As we are told that base of pyramid is square and is 62 meters and height of pyramid is 62 meters.

Upon substituting our given values in slant height formula we will get,

`\text{h}=\sqrt{62^2+((62)/(2))^2}`

`\text{h}=\sqrt{62^2+(62^2)/(2^2)}`

`\text{h}=\sqrt{3844+(3844)/(4)}`

`\text{h}=√(3844+961)`

`\text{h}=√(4805)`

`\text{h}=69.318107\approx 69.3`

Therefore, the height of the each triangular face is approximately 69.3 meters.