Answer: the surface area of the composite figure is 195 square units.
Step-by-step, explanation/work:
To find the surface area of the composite figure, we need to calculate the surface area of the rectangular prism and the square pyramid separately, and then add them together.
Let's first find the surface area of the rectangular prism. A rectangular prism has six faces, each of which is a rectangle. The formula for the surface area of a rectangular prism is:
SA = 2lw + 2lh + 2wh
where l, w, and h are the length, width, and height of the rectangular prism.
Let's assume that the rectangular prism has dimensions of 4 units by 6 units by 8 units. Then, the surface area of the rectangular prism is:
SA_rectangular prism = 2(4*6) + 2(4*8) + 2(6*8) = 120 square units
Next, let's find the surface area of the square pyramid. A square pyramid has five faces: a square base and four triangular faces. To find the surface area of a square pyramid, we need to find the area of the square base and the area of each of the four triangular faces, and then add them together. The formula for the surface area of a square pyramid is:
SA = l^2 + 2lh
where l is the length of one side of the square base, and h is the height of the pyramid.
Let's assume that the square pyramid has a base of 5 units and a height of 10 units. Then, the surface area of the square pyramid is:
SA_square pyramid = 5^2 + 2(5*10) = 75 square units
Now that we have calculated the surface area of both the rectangular prism and the square pyramid, we can add them together to find the total surface area of the composite figure:
SA_composite figure = SA_rectangular prism + SA_square pyramid
SA_composite figure = 120 + 75
SA_composite figure = 195 square units