When finding the surface area of a composite figure, which in this case consists of a square pyramid sitting on top of a cube, I know that the first step is to find the surface area of the cube, but after that I would find the surface area of the square pyramid, but do I calculate the area of the base of the square pyramid, since I already calculated it when finding the surface area of the cube.

In most cases, when finding the surface area such as your shape, we find the surface area of only the exposed surfaces, so the top of the cube and the base of the pyramid would not be included at all.

I would find the 5 visible sides of the cube + the 4 isosceles triangle of the pyramid.

But, that may just be my opinion , I would check with your teacher.

When finding the surface area of a composite figure, it is important to calculate the individual surface areas of each component and then add them together.

In your case, you correctly mentioned that you need to find the surface area of the cube and the square pyramid separately.

To calculate the surface area of the cube, you would need to find the area of each face and sum them up. Since all faces of a cube are congruent squares, you only need to calculate the area of one face by multiplying the length of one side of the cube by itself. The surface area of the cube would then be the area of one face multiplied by 6, as a cube has 6 faces.

Next, you need to calculate the surface area of the square pyramid. The surface area of a pyramid consists of the area of the base and the areas of the triangular faces. Since the pyramid in your composite figure has a square base, you do not need to calculate the base separately, as you have already calculated it as part of the surface area of the cube. However, you still need to calculate the areas of the triangular faces and sum them up. To calculate the area of a triangular face, you need the length of the base and the height of the triangle.

After calculating the surface area of the cube and the triangular faces of the square pyramid, you can simply add them together to find the total surface area of the composite figure.

Therefore, in summary, you do not need to calculate the area of the base of the square pyramid separately since it is already included when calculating the surface area of the cube. Instead, focus on finding the area of the triangular faces of the pyramid and add it to the surface area of the cube to get the total surface area of the composite figure.

Yes, you are correct that the first step in finding the surface area of a composite figure consisting of a square pyramid on top of a cube is to find the surface area of the cube. However, for the square pyramid, you will need to calculate the area of its base separately, even though it may have the same dimensions as the base of the cube.

The reason for this is that surface area is a measurement of the total area of all the individual faces of the composite figure. The base of the pyramid and the top face of the cube are separate faces, even though they may have the same dimensions.

To calculate the surface area of the composite figure, you would:

1. Find the surface area of the cube by summing the areas of all six faces.
2. Calculate the area of the base of the square pyramid separately, using its specific dimensions.
3. Find the lateral surface area of the square pyramid, which includes the four triangular faces (excluding the base).
4. Add the surface area of the cube, the area of the base of the square pyramid, and the lateral surface area of the square pyramid together to get the total surface area of the composite figure.