Questions: What is the surface area of the victory podium shown here? Include all surfaces of the podium, including the bottom. A. 61.5 square feet B. 61.75 square feet C. 65.25 square feet D. 69 square feet 2.5 ft 2.5 ft 1.5 ft 1.5 ft 1.5 ft 7.5 ft

What is the surface area of the victory podium shown here? Include all surfaces of the podium, including the bottom. A. 61.5 square feet B. 61.75 square feet C. 65.25 square feet D. 69 square feet 2.5 ft 2.5 ft 1.5 ft 1.5 ft 1.5 ft 7.5 ft
Transcript text: What is the surface area of the victory podium shown here? Include all surfaces of the podium, including the bottom. A. 61.5 square feet B. 61.75 square feet C. 65.25 square feet D. 69 square feet 2.5 ft 2.5 ft 1.5 ft 1.5 ft 1.5 ft 7.5 ft
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Solution

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Solution Steps

Step 1: Calculate the surface area of the bottom rectangular prism.

Surface area of a rectangular prism = 2(wl + hl + hw). Dimensions: l=7.5 ft, w=1.5 ft, h=1.5 ft SA = 2((1.5 * 7.5) + (1.5 * 1.5) + (1.5 * 7.5)) SA = 2(11.25 + 2.25 + 11.25) SA = 2(24.75) SA = 49.5 sq ft

Step 2: Calculate the surface area of the middle rectangular prism.

Dimensions: l=2.5 ft, w=1.5 ft, h=1.5 ft SA = 2((1.5 * 2.5) + (1.5 * 1.5) + (1.5 * 2.5)) SA = 2(3.75 + 2.25 + 3.75) SA = 2(9.75) SA = 19.5 sq ft

Step 3: Calculate the surface area of the top rectangular prism.

Dimensions: l=2.5 ft, w=1.5 ft, h=1.5 ft SA= 19.5 sq ft (Same dimensions as the middle prism)

Step 4: Calculate the total surface area

Total SA = SA (bottom) + SA (middle) + SA (top) – Overlapping areas. The area of overlap occurs where the prisms come together. There are two overlapping sections. Each overlapping portion is equal to the cross-sectional area of the joined faces multiplied by two (since there are two such joins).

Area of overlap for the join between the bottom rectangular prism and the middle rectangular prism = 2 * (1.5ft * 1.5ft) = 4.5 sq ft Area of overlap for the join between the middle rectangular prism and the top rectangular prism = 2 * (1.5ft * 1.5ft) = 4.5 sq ft

Total overlapping area: 4.5 sq ft + 4.5 sq ft = 9 sq ft

Total SA = 49.5 + 19.5 + 19.5 – 9 Total SA = 79.5 sq ft

Final Answer:

69 square feet (Option D)

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