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Vitek1552 [10]
3 years ago
14

Calculate the height of the square based pyramid

Mathematics
1 answer:
Reika [66]3 years ago
3 0

<u>Given:</u>

A square pyramid with a base edge length of 8 m and a slant height of 12 m.

<u>To find:</u>

The height of the pyramid.

<u>Solution:</u>

A right-angled triangle can be formed with the slant height, the height, and half the length of the base edge.

The slant height of the pyramid is 12 m long and is the hypotenuse of the right-angled triangle.

Assume the height of the pyramid is x and half the length of the base edge is \frac{1}{2} (8) = 4 m.

According to the Pythagorean theorem, the square of the hypotenuse will be equal to the sum of the squares of the other two sides.

The hypotenuse measures 12 m while the other two sides measure 4 m and x m each.

12^{2} = 4^{2} +x^{2} .

x^{2} = 12^{2} - 4^{2} = 144-16=128.

x=\sqrt{128} = 11.313 m.

The height of the square-based pyramid is 11.313 m.

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