Surface area calculation practice for rectangular prisms with real-world application.
Worksheet with nine rectangular prisms and a word problem asking to find the surface area of each, including one gift box scenario.
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Show Answer Key & Explanations
Step-by-step solution for: Surface Area Worksheets | Area worksheets, Volume worksheets, Area ...
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Show Answer Key & Explanations
Step-by-step solution for: Surface Area Worksheets | Area worksheets, Volume worksheets, Area ...
To find the surface area of a rectangular prism, we need to find the total area of all six faces. The formula is:
Surface Area = 2(length × width + length × height + width × height)
Let’s solve each problem one by one.
---
1) Dimensions: 9 mm, 5 mm, 13 mm
SA = 2(9×5 + 9×13 + 5×13)
= 2(45 + 117 + 65)
= 2(227)
= 454 mm²
---
2) Dimensions: 20 cm, 4 cm, 6 cm
SA = 2(20×4 + 20×6 + 4×6)
= 2(80 + 120 + 24)
= 2(224)
= 448 cm²
---
**3) Dimensions: 8 ft, 5 m, 14 m → Wait! Units are mixed (ft and m). But looking at the diagram, it's likely all in meters? Or maybe typo? Let’s check the image again — actually, in the original image, #3 shows: 8 ft, 5 m, 14 m — that can’t be right for a single prism. But since this is a worksheet, probably all units are meant to be consistent. Looking closely: the label says “8 ft” on one edge, but others say “m”. That must be an error. However, in standard worksheets like this, if not specified, assume same unit. But here, two are “m”, one is “ft”. Since 8 ft ≈ 2.44 m, but that would make calculation messy. Alternatively, perhaps it’s a misprint and should be 8 m? Let’s look at other problems — they use consistent units per problem. So likely, #3 has a typo. But wait — looking back at user’s image description: “8 ft, 5 m, 14 m” — that doesn’t make sense. Actually, re-examining: in many such worksheets, sometimes the unit is written once per figure. In #3, the vertical side says “14 m”, front bottom says “5 m”, and depth says “8 ft” — that’s inconsistent. But since this is a math worksheet for kids, it’s almost certainly a typo and should be 8 m. I’ll proceed assuming all are in meters. If not, the answer would be wrong, but given context, 8 m is intended.)
Assume: 8 m, 5 m, 14 m
SA = 2(8×5 + 8×14 + 5×14)
= 2(40 + 112 + 70)
= 2(222)
= 444 m²
*(Note: If 8 ft was intentional, we’d convert: 8 ft = 2.4384 m, then calculate — but that’s too advanced for this level. So we go with 8 m.)*
---
4) Dimensions: 14 ft, 17 ft, 4 ft
SA = 2(14×17 + 14×4 + 17×4)
= 2(238 + 56 + 68)
= 2(362)
= 724 ft²
---
5) Dimensions: 4 in, 9 in, 13 in
SA = 2(4×9 + 4×13 + 9×13)
= 2(36 + 52 + 117)
= 2(205)
= 410 in²
---
6) Dimensions: 8 mm, 9 mm, 14 mm
SA = 2(8×9 + 8×14 + 9×14)
= 2(72 + 112 + 126)
= 2(310)
= 620 mm²
---
7) Dimensions: 7 cm, 12 cm, 4 cm
SA = 2(7×12 + 7×4 + 12×4)
= 2(84 + 28 + 48)
= 2(160)
= 320 cm²
---
8) Dimensions: 12 in, 4 in, 6 in
SA = 2(12×4 + 12×6 + 4×6)
= 2(48 + 72 + 24)
= 2(144)
= 288 in²
---
9) Dimensions: 4 ft, 15 ft, 8 ft
SA = 2(4×15 + 4×8 + 15×8)
= 2(60 + 32 + 120)
= 2(212)
= 424 ft²
---
10) Gift box: length 20 cm, width 14 cm, height 10 cm
SA = 2(20×14 + 20×10 + 14×10)
= 2(280 + 200 + 140)
= 2(620)
= 1240 cm²
This is how much paper you need to wrap the gift box.
---
Final Answer:
1) 454 mm²
2) 448 cm²
3) 444 m² *(assuming 8 ft was meant to be 8 m)*
4) 724 ft²
5) 410 in²
6) 620 mm²
7) 320 cm²
8) 288 in²
9) 424 ft²
10) 1240 cm²
Surface Area = 2(length × width + length × height + width × height)
Let’s solve each problem one by one.
---
1) Dimensions: 9 mm, 5 mm, 13 mm
SA = 2(9×5 + 9×13 + 5×13)
= 2(45 + 117 + 65)
= 2(227)
= 454 mm²
---
2) Dimensions: 20 cm, 4 cm, 6 cm
SA = 2(20×4 + 20×6 + 4×6)
= 2(80 + 120 + 24)
= 2(224)
= 448 cm²
---
**3) Dimensions: 8 ft, 5 m, 14 m → Wait! Units are mixed (ft and m). But looking at the diagram, it's likely all in meters? Or maybe typo? Let’s check the image again — actually, in the original image, #3 shows: 8 ft, 5 m, 14 m — that can’t be right for a single prism. But since this is a worksheet, probably all units are meant to be consistent. Looking closely: the label says “8 ft” on one edge, but others say “m”. That must be an error. However, in standard worksheets like this, if not specified, assume same unit. But here, two are “m”, one is “ft”. Since 8 ft ≈ 2.44 m, but that would make calculation messy. Alternatively, perhaps it’s a misprint and should be 8 m? Let’s look at other problems — they use consistent units per problem. So likely, #3 has a typo. But wait — looking back at user’s image description: “8 ft, 5 m, 14 m” — that doesn’t make sense. Actually, re-examining: in many such worksheets, sometimes the unit is written once per figure. In #3, the vertical side says “14 m”, front bottom says “5 m”, and depth says “8 ft” — that’s inconsistent. But since this is a math worksheet for kids, it’s almost certainly a typo and should be 8 m. I’ll proceed assuming all are in meters. If not, the answer would be wrong, but given context, 8 m is intended.)
Assume: 8 m, 5 m, 14 m
SA = 2(8×5 + 8×14 + 5×14)
= 2(40 + 112 + 70)
= 2(222)
= 444 m²
*(Note: If 8 ft was intentional, we’d convert: 8 ft = 2.4384 m, then calculate — but that’s too advanced for this level. So we go with 8 m.)*
---
4) Dimensions: 14 ft, 17 ft, 4 ft
SA = 2(14×17 + 14×4 + 17×4)
= 2(238 + 56 + 68)
= 2(362)
= 724 ft²
---
5) Dimensions: 4 in, 9 in, 13 in
SA = 2(4×9 + 4×13 + 9×13)
= 2(36 + 52 + 117)
= 2(205)
= 410 in²
---
6) Dimensions: 8 mm, 9 mm, 14 mm
SA = 2(8×9 + 8×14 + 9×14)
= 2(72 + 112 + 126)
= 2(310)
= 620 mm²
---
7) Dimensions: 7 cm, 12 cm, 4 cm
SA = 2(7×12 + 7×4 + 12×4)
= 2(84 + 28 + 48)
= 2(160)
= 320 cm²
---
8) Dimensions: 12 in, 4 in, 6 in
SA = 2(12×4 + 12×6 + 4×6)
= 2(48 + 72 + 24)
= 2(144)
= 288 in²
---
9) Dimensions: 4 ft, 15 ft, 8 ft
SA = 2(4×15 + 4×8 + 15×8)
= 2(60 + 32 + 120)
= 2(212)
= 424 ft²
---
10) Gift box: length 20 cm, width 14 cm, height 10 cm
SA = 2(20×14 + 20×10 + 14×10)
= 2(280 + 200 + 140)
= 2(620)
= 1240 cm²
This is how much paper you need to wrap the gift box.
---
Final Answer:
1) 454 mm²
2) 448 cm²
3) 444 m² *(assuming 8 ft was meant to be 8 m)*
4) 724 ft²
5) 410 in²
6) 620 mm²
7) 320 cm²
8) 288 in²
9) 424 ft²
10) 1240 cm²
Parent Tip: Review the logic above to help your child master the concept of volume and surface area of rectangular prism worksheet.
