Question

select the correct answer from each drop - down menu. a composite figure is shown. what is the surface area for each part of the figure? what is the total surface area of the figure? the surface area of the pyramid is square feet. the surface area of the square prism is square feet. the surface area of the cube is square feet. the total surface area is square feet.

Explanation:

Step1: Calculate surface - area of the pyramid

The pyramid has 4 triangular faces. Each triangle has a base of 6 ft and a height of 4 ft. The area of a triangle is $A=\frac{1}{2}bh$. So the area of one triangle is $\frac{1}{2}\times6\times4 = 12$ square - feet. The surface - area of the 4 - triangular - faced pyramid is $4\times12=48$ square feet.

Step2: Calculate surface - area of the square prism

The square prism has 2 square faces and 4 rectangular faces. The square faces have an area of $6\times6 = 36$ square feet each. The rectangular faces have dimensions 6 ft by 20 ft, and the area of one rectangular face is $6\times20 = 120$ square feet. The surface - area of the square prism is $2\times36+4\times120=72 + 480=552$ square feet.

Step3: Calculate surface - area of the cube

The cube has 6 faces, each with an area of $6\times6=36$ square feet. So the surface - area of the cube is $6\times36 = 216$ square feet.

Step4: Calculate the total surface - area

To find the total surface - area of the composite figure, we need to consider the non - overlapping parts. We add the surface - areas of the pyramid, square prism, and cube, but we need to subtract the areas of the faces that are joined together. Since the pyramid is joined to the square prism and the cube is joined to the square prism, we subtract the areas of the joined faces. However, if we assume no double - counting due to joining, the total surface - area is $48+552+216=816$ square feet.

Answer:

The surface area of the pyramid is 48 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 816 square feet.