Question

Find the slant height of the square pyramid with measures of 12 cm and 10 cm
15.6 cm
13 cm
244 cm
169 cm

Answer 1

12 is the height and 10 is the abse length

Answer 2

To find the slant height of a square pyramid, we need to know the height of the pyramid and the length of the base. In this case, we assume that the 12 cm is the length of a side of the square base, and the 10 cm is the height of the pyramid.

The slant height \( l \) of a pyramid can be calculated using the Pythagorean theorem, where:

1. The height \( h \) is one leg of a right triangle.
2. Half the base length \( \frac{b}{2} \) is the other leg.
3. The slant height \( l \) is the hypotenuse.

For a square pyramid:
- The base length \( b = 12 \) cm, so \( \frac{b}{2} = \frac{12}{2} = 6 \) cm.
- The height \( h = 10 \) cm.

Now we can apply the Pythagorean theorem:

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

Substituting in the values:

\[
l = \sqrt{10^2 + 6^2}
\]
\[
l = \sqrt{100 + 36}
\]
\[
l = \sqrt{136}
\]
\[
l \approx 11.66 \text{ cm}
\]

This value does not match any of your multiple-choice answers. Please double-check the values provided (12 cm and 10 cm) and ensure they correspond to the base length and height of the pyramid. Based on the provided values, the calculated slant height is approximately 11.66 cm.

Answer 3

Thank you for clarifying! In that case, with the height of the pyramid being 12 cm and the base length being 10 cm, let's find the slant height again.

1. The height \( h = 12 \) cm.
2. The base length \( b = 10 \) cm, so half of the base length \( \frac{b}{2} = \frac{10}{2} = 5 \) cm.

Now we can calculate the slant height \( l \) using the Pythagorean theorem:

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

Substituting the values:

\[
l = \sqrt{12^2 + 5^2}
\]
\[
l = \sqrt{144 + 25}
\]
\[
l = \sqrt{169}
\]
\[
l = 13 \, \text{cm}
\]

So the slant height of the square pyramid is **13 cm**. This matches one of your provided options.