Question

You are building a model of a square pyramid. The side length of the base of the model is 30 cm. The height is 23 cm. What is the slant height of the model​ pyramid?
30 cm
Slant Height
23 cm
​(This figure is not drawn to​ scale.)
Question content area bottom
Part 1
The slant height of the model pyramid is about
  
enter your response here cm.
​(Round to the nearest tenth as​ needed.)

Answer 1

To find the slant height of the square pyramid, we can use the Pythagorean theorem. The slant height (\( l \)), the height of the pyramid (\( h \)), and half of the base length (\( \frac{b}{2} \)) form a right triangle.

1. The height of the pyramid (\( h \)) is given as 23 cm.
2. The side length of the base (\( b \)) is given as 30 cm, so half of the base length is \( \frac{b}{2} = \frac{30}{2} = 15 \) cm.

Now we can use the Pythagorean theorem:

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

Substituting the values we have:

\[
l^2 = 23^2 + 15^2
\]

Calculating \( 23^2 \) and \( 15^2 \):

\[
23^2 = 529
\]
\[
15^2 = 225
\]

Now adding these values:

\[
l^2 = 529 + 225 = 754
\]

Next, we take the square root to find \( l \):

\[
l = \sqrt{754} \approx 27.5 \text{ cm}
\]

Rounding to the nearest tenth, the slant height of the model pyramid is approximately **27.5 cm**.