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 pr square feet. the surface area of the cube is square feet. the total surface area is e feet. (options for some blanks: 60, 48, 96)

Explanation:

Step1: Calculate pyramid surface area

The pyramid has a square base (6 ft × 6 ft) but we only calculate its 4 triangular faces (since the base is attached to the prism, not exposed). Each triangular face area: $\frac{1}{2} \times 6 \times 4 = 12$ sq ft. Total for 4 faces: $4 \times 12 = 48$ sq ft.

Step2: Calculate square prism surface area

The prism is a rectangular prism with dimensions 6 ft × 6 ft × 20 ft. We exclude one 6×6 face (attached to cube) and one 6×6 face (attached to pyramid). Surface area formula: $2(lw + lh + wh) - 2(6 \times 6)$.
First, full surface area: $2(6 \times 6 + 6 \times 20 + 6 \times 20) = 2(36 + 120 + 120) = 2(276) = 552$ sq ft.
Subtract the two hidden faces: $552 - 2 \times 36 = 552 - 72 = 480$ sq ft.

Step3: Calculate cube surface area

The cube is 6 ft × 6 ft × 6 ft, with one 6×6 face attached to the prism (not exposed). Surface area: $6(6 \times 6) - 6 \times 6 = 6 \times 36 - 36 = 216 - 36 = 180$ sq ft.

Step4: Calculate total surface area

Sum the exposed surface areas: $48 + 480 + 180 = 708$ sq ft.

Answer:

The surface area of the pyramid is 48 square feet.
The surface area of the square prism is 480 square feet.
The surface area of the cube is 180 square feet.
The total surface area is 708 square feet.