5. the faces of this square pyramid are equilateral triangles. draw a net of the pyramid and use it to find…

Explanation:

Step1: Identify the components of the square pyramid

The pyramid consists of one square base and four equilateral triangular faces.

Step2: Calculate the area of the square base

The side length $s$ is $12\text{ ft}$. $$A_{base} = s^{2} = 12^{2} = 144\text{ ft}^{2}$$

Step3: Calculate the area of one triangular face

The base $b$ is $12\text{ ft}$ and the slant height $h$ is $10.4\text{ ft}$. $$A_{triangle} = \frac{1}{2} \times b \times h = \frac{1}{2} \times 12 \times 10.4 = 62.4\text{ ft}^{2}$$

Step4: Calculate the total lateral area

Multiply the area of one triangle by the four faces. $$A_{lateral} = 4 \times 62.4 = 249.6\text{ ft}^{2}$$

Step5: Calculate the total surface area

Sum the area of the base and the lateral area. $$SA = A_{base} + A_{lateral} = 144 + 249.6 = 393.6\text{ ft}^{2}$$

Answer:

The total surface area is $393.6\text{ ft}^{2}$.