select the correct answer from each drop - down menu. a composite figure is shown. what is the surface area…

Explanation:

Step1: Calculate surface - area of the cube

A cube has 6 equal - sized faces. Each face of the cube has an area of $A_{face}=6\times6 = 36$ square feet. So the surface area of the cube $S_{cube}=6\times36=216$ square feet.

Step2: Calculate surface - area of the square prism

The square prism has two square faces with area $A_{square}=6\times6 = 36$ square feet each, and four rectangular faces with area $A_{rect}=6\times20 = 120$ square feet each. So the surface area of the square prism $S_{prism}=2\times36 + 4\times120=72 + 480 = 552$ square feet.

Step3: Calculate surface - area of the pyramid

The base of the pyramid is a square with area $A_{base}=6\times6 = 36$ square feet. The slant height of the pyramid $l = 4$ feet. Each triangular face of the pyramid has an area of $A_{triangle}=\frac{1}{2}\times6\times4=12$ square feet. There are 4 triangular faces. So the surface area of the pyramid $S_{pyramid}=36+4\times12=36 + 48 = 84$ square feet.

Step4: Calculate the total surface area

The total surface area $S_{total}=S_{cube}+S_{prism}+S_{pyramid}- 2\times6\times6$ (we subtract $2\times6\times6$ because the two faces where the cube and the prism, and the prism and the pyramid are joined are not part of the outer - surface). $S_{total}=216+552 + 84-72=780$ square feet.

Answer:

The surface area of the pyramid is 84 square feet. The surface area of the square prism is 552 square feet. The surface area of the cube is 216 square feet. The total surface area is 780 square feet.