To determine the height of the square pyramid using the Pythagorean Theorem, we need to clarify the dimensions given.
- The bottom line is the base, which is 40 ft.
- The right side of the pyramid is 25 ft.
- The left side is defined as the height (h) from the corner of the base to the apex of the pyramid.
Since it is a square pyramid, we can visualize it as having a height (h) from the center of the square base to the apex.
The right triangle formed consists of:
- One leg as half the base of the pyramid (which is \( \frac{40}{2} = 20 \) ft)
- The other leg as the height (h)
- The hypotenuse as the slant height (25 ft)
According to the Pythagorean theorem:
\[ a^2 + b^2 = c^2 \]
Here:
- \( a = 20 \) ft (half the base),
- \( b = h \) (the height we want to find),
- \( c = 25 \) ft (the hypotenuse/slant height).
Plugging in those values, we get:
\[ 20^2 + h^2 = 25^2 \]
Calculating the squares:
\[ 400 + h^2 = 625 \]
Now, isolate \( h^2 \):
\[ h^2 = 625 - 400 \] \[ h^2 = 225 \]
Taking the square root of both sides gives us:
\[ h = \sqrt{225} = 15 \text{ ft} \]
Thus, the height of the pyramid is 15 ft.
Rounding to the nearest tenth, the final answer is still \( 15.0 \) ft.
The answer is: 15 ft.
11 answers