Asked by liquidlew
Find the slant height of the square pyramid. Round to the nearest whole inch, if necessary.
Point is 12 inc.
Baseline is 18 inc.
(1 point)
Responses
8 in.
8 in.
15 in.
15 in.
13 in.
13 in.
6 in.
6 in.
Answers
Answered by
GPT-4o mini
To find the slant height of a square pyramid, we can use the Pythagorean theorem. The slant height, \( l \), is the hypotenuse of a right triangle formed by:
1. The height of the pyramid (the distance from the apex to the center of the base).
2. Half of the length of the base (which is half of the baseline).
Given:
- Point (height) = 12 inches
- Baseline (length of one side of the base) = 18 inches
First, we find half of the baseline:
\[
\text{Half of baseline} = \frac{18 \text{ in}}{2} = 9 \text{ in}
\]
Now we can use the Pythagorean theorem:
\[
l = \sqrt{(\text{Height})^2 + (\text{Half of base})^2}
\]
Substituting in the values:
\[
l = \sqrt{(12 \text{ in})^2 + (9 \text{ in})^2}
\]
\[
l = \sqrt{144 \text{ in}^2 + 81 \text{ in}^2}
\]
\[
l = \sqrt{225 \text{ in}^2}
\]
\[
l = 15 \text{ in}
\]
Thus, the slant height of the square pyramid is **15 inches**.
1. The height of the pyramid (the distance from the apex to the center of the base).
2. Half of the length of the base (which is half of the baseline).
Given:
- Point (height) = 12 inches
- Baseline (length of one side of the base) = 18 inches
First, we find half of the baseline:
\[
\text{Half of baseline} = \frac{18 \text{ in}}{2} = 9 \text{ in}
\]
Now we can use the Pythagorean theorem:
\[
l = \sqrt{(\text{Height})^2 + (\text{Half of base})^2}
\]
Substituting in the values:
\[
l = \sqrt{(12 \text{ in})^2 + (9 \text{ in})^2}
\]
\[
l = \sqrt{144 \text{ in}^2 + 81 \text{ in}^2}
\]
\[
l = \sqrt{225 \text{ in}^2}
\]
\[
l = 15 \text{ in}
\]
Thus, the slant height of the square pyramid is **15 inches**.