Explanation:
To find the surface area of a rectangular prism, we use the formula:
Surface Area = 2 × (length × width + length × height + width × height)
We need to identify the three dimensions for each prism: length, width, and height. The order doesn’t matter as long as we use all three different side lengths.
Let’s go one by one:
1) Dimensions: 11 m, 7 m, 2 m
SA = 2×(11×7 + 11×2 + 7×2) = 2×(77 + 22 + 14) = 2×113 =
226 m²
2) Dimensions: 12 ft, 10 ft, 9 ft
SA = 2×(12×10 + 12×9 + 10×9) = 2×(120 + 108 + 90) = 2×318 =
636 ft²
3) Dimensions: 4 in, 8 in, 3 in
SA = 2×(4×8 + 4×3 + 8×3) = 2×(32 + 12 + 24) = 2×68 =
136 in²
4) Dimensions: 16 cm, 11 cm, 10 cm
SA = 2×(16×11 + 16×10 + 11×10) = 2×(176 + 160 + 110) = 2×446 =
892 cm²
5) Dimensions: 10 cm, 4 cm, 3 cm
SA = 2×(10×4 + 10×3 + 4×3) = 2×(40 + 30 + 12) = 2×82 =
164 cm²
6) Dimensions: 15 mm, 11 mm, 5 mm
SA = 2×(15×11 + 15×5 + 11×5) = 2×(165 + 75 + 55) = 2×295 =
590 mm²
7) Dimensions: 13 mm, 11 mm, 2 mm
SA = 2×(13×11 + 13×2 + 11×2) = 2×(143 + 26 + 22) = 2×191 =
382 mm²
8) Dimensions: 14 m, 9 m, 8 m
SA = 2×(14×9 + 14×8 + 9×8) = 2×(126 + 112 + 72) = 2×310 =
620 m²
9) Dimensions: 9 ft, 13 ft, 3 ft
SA = 2×(9×13 + 9×3 + 13×3) = 2×(117 + 27 + 39) = 2×183 =
366 ft²
10) Lisa’s box: 12 cm × 8 cm × 18 cm
SA = 2×(12×8 + 12×18 + 8×18) = 2×(96 + 216 + 144) = 2×456 =
912 cm²
Double-checking a couple:
- #1: 11×7=77, 11×2=22, 7×2=14 → sum=113 → ×2=226
✔
- #10: 12×8=96, 12×18=216, 8×18=144 → sum=456 → ×2=912
✔
All calculations are correct.
Final Answer:
1) 226 m²
2) 636 ft²
3) 136 in²
4) 892 cm²
5) 164 cm²
6) 590 mm²
7) 382 mm²
8) 620 m²
9) 366 ft²
10) 912 cm²
Parent Tip: Review the logic above to help your child master the concept of volume and surface area of a rectangular prism worksheet answers.
