Question

1. using the following diagram

12 feet
10 feet
10 feet
a. find the height of the triangle faces using the pythagorean theorem.

Explanation:

Step1: Identify right - triangle sides

The base of the right - triangle formed on the face is half of the base side length of the pyramid base. The base side length of the pyramid base is 10 feet, so the base of the right - triangle on the face $a = \frac{10}{2}=5$ feet, and the slant height (hypotenuse) $c = 12$ feet.

Step2: Apply Pythagorean Theorem

The Pythagorean Theorem is $c^{2}=a^{2}+b^{2}$, where $b$ is the height of the triangle face we want to find. Rearranging for $b$, we get $b=\sqrt{c^{2}-a^{2}}$. Substitute $a = 5$ and $c = 12$ into the formula: $b=\sqrt{12^{2}-5^{2}}=\sqrt{144 - 25}=\sqrt{119}\approx10.91$ feet.

Answer:

$\sqrt{119}\approx10.91$ feet