Question

Communicate and Justify How does finding the area of one face of a square pyramid that is made up of equilateral triangles help you find the surface area of the square pyramid?​

Answer 1

Finding the area of one face of a square pyramid made up of equilateral triangles helps you find the surface area of the pyramid because it gives you the area of one of the triangular faces. Since a square pyramid has four identical triangular faces, you can simply multiply the area of one face by 4 to find the combined area of all the triangular faces.

To find the surface area of the square pyramid, you also need to find the area of the square base. Once you have the area of the base and the combined area of the four triangular faces, you can add these areas together to find the total surface area of the pyramid.

Here's a step-by-step process:

1. Find the area of one equilateral triangle face using the formula: (side length^2 * √3) / 4
2. Multiply the area of one triangle face by 4 to find the combined area of all four triangular faces.
3. Find the area of the square base using the formula: side length^2
4. Add the combined area of the triangular faces and the area of the square base to find the total surface area of the square pyramid.