Question

1. using the following diagram

12 feet
10 feet
10 feet

a. find the height of the triangle faces using the pythagorean theorem.

b. draw a net of the square pyramid including dimensions.

Explanation:

Step1: Identify right - triangle sides

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

Step2: Apply Pythagorean Theorem

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

For part b, as this is a text - based response, a verbal description of the net is provided:
The net of a square pyramid consists of a square in the center with side length 10 feet. Attached to each side of the square are 4 congruent triangles. The base of each triangle is 10 feet (the side of the square), and the height of each triangle (slant height) is 12 feet.

Answer:

a. The height of the triangle faces is $\sqrt{119}\approx10.91$ feet.
b. The net consists of a 10 - foot by 10 - foot square and 4 congruent triangles with base 10 feet and height 12 feet.