Find Surface Area from Every Face in a Net
Use the supplied rectangular-prism edge lengths to list all face areas.
About 25 minutes, plus any extended practice
Supplied materials
- Paper and a pencil; drawing and spoken explanations are welcome. An adult may read directions and options aloud.
- Supplied worked-case record: For edges 2,3,5 cm, opposite face pairs have areas 6,10,15 square cm.
- All quantities and shape descriptions are supplied in the worked example and questions; no purchase or personal information is needed.
Learn the idea
Surface area counts the flat areas of a solid’s boundary faces. A rectangular prism has three pairs of equal-area faces. Add all six, or double the sum of the three distinct products. Volume counts the interior and uses a different formula and unit. A face shared inside a composite solid is not exposed surface.
Use the supplied rectangular-prism edge lengths to list all face areas. Add each exposed face exactly once and report square units. Compare with volume to explain why multiplying all three lengths does not give the boundary area.
List all six faces or clearly account for three pairs. Surface area is square units; volume is cubic units. Sketch a six-rectangle net and write each face’s two edge dimensions.
- Sketch a six-rectangle net and write each face’s two edge dimensions.
- Work through the supplied example and label what each number or attribute represents.
- Use the supplied rectangular-prism edge lengths to list all face areas.
- Answer the check, then try the three changed-input practice questions and explain one correction.
See the method in action
For edges 2,3,5 cm, opposite face pairs have areas 6,10,15 square cm. Surface area is 2(6+10+15)=62 square cm. Volume would be thirty cubic cm. A paper net would contain all six rectangles with these areas before folding. List all six faces or clearly account for three pairs. Surface area is square units; volume is cubic units. Sketch a six-rectangle net and write each face’s two edge dimensions.
Check your reasoning
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Helpful tips
- List all six faces or clearly account for three pairs.
- Surface area is square units; volume is cubic units.
See the answer and explanation
52
Sum all three opposite face pairs once each. The result is 52.
Take it further
Edges 3,5,7 give surface area 142 square units and volume 105 cubic units.
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