Final answer:
After calculating the surface areas, composite figure A, consisting of two rectangular prisms with dimensions 2x1x1 and 2x2x2, has the greatest surface area, which totals 34.
Step-by-step explanation:
To determine which composite figure has the greatest surface area, we will calculate the surface area of each option provided. A surface area of a rectangular prism is calculated by finding the area of all the faces and adding them together; for a cube, it will be 6 times one face as all sides are equal.
A. Surface area function for rectangular prisms is SA = 2lw + 2lh + 2wh, so for the first prism it's SA1 = 2(2)(1) + 2(2)(1) + 2(1)(1) = 4 + 4 + 2 = 10. The second prism is SA2 = 2(2)(2) + 2(2)(2) + 2(2)(2) = 8 + 8 + 8 = 24. Total Surface Area (SA) for A is SA1 + SA2 = 10 + 24 = 34.
B. Surface area for the single rectangular prism SA = 2(1)(1) + 2(1)(2) + 2(1)(2) = 2 + 4 + 4 = 10.
C. The first prism SA1 = 2(2)(2) + 2(2)(1) + 2(2)(1) = 8 + 4 + 4 = 16, and the second prism SA2 is the same as in A, which is 10. Total SA for C is SA1 + SA2 = 16 + 10 = 26.
D. Surface area for the cube SA = 6(2)(2) = 24.
Comparing surface areas: A (34) > C (26) > D (24) > B (10). So, composite figure A has the greatest surface area.