Question

The Great Pyramid of Giza in Egypt has a square base with edge length of 245.5 m and a slant height of 190.2 m. Find the height of the pyramid

Answer 1

To find the height of the Great Pyramid of Giza, we can use the Pythagorean theorem. The pyramid has a square base, and we can visualize it as a right triangle formed by:

1. The height of the pyramid (h).
2. The slant height (l), which is the hypotenuse of the triangle.
3. Half of the base length (b/2), which forms one leg of the triangle.

Given:

- The edge length (diagonal of the base) of the pyramid is \( b = 245.5 \, \text{m} \).
- The slant height \( l = 190.2 \, \text{m} \).

First, we need to find half of the base length:

\[
\frac{b}{2} = \frac{245.5}{2} = 122.75 \, \text{m}
\]

Now we can apply the Pythagorean theorem:

\[
l^2 = h^2 + \left(\frac{b}{2}\right)^2
\]

Substituting the known values:

\[
(190.2)^2 = h^2 + (122.75)^2
\]

Calculating each square:

\[
190.2^2 = 36176.04
\]
\[
122.75^2 = 15068.0625
\]

Substituting these values into the equation:

\[
36176.04 = h^2 + 15068.0625
\]

Now, solve for \( h^2 \):

\[
h^2 = 36176.04 - 15068.0625
\]
\[
h^2 = 21107.9775
\]

Finally, take the square root to find \( h \):

\[
h = \sqrt{21107.9775} \approx 145.4 \, \text{m}
\]

Thus, the height of the Great Pyramid of Giza is approximately **145.4 meters**.