What you’ll learn
Calculate surface area using nets.
Key idea
Each face area has a congruent opposite partner; total surface area is a sum of areas, not a volume product.
A closed prism has six faces with three opposite pairs; surface area is not the product of three edge lengths.
Worked example
Enter the exact value or ordered values in the format requested below.
A rectangular-prism net shows two 2×3, two 2×9, and two 3×9 cm faces. Enter numerical total surface area in square centimeters.
- The three opposite face-pair areas are 2×3=6, 2×9=18, and 3×9=27 cm².
- Every face type occurs twice; total surface area is 2(6+18+27)=102 cm².
Answer: 102
Quick Check
Evaluate a worked attempt at calculate surface area using nets, identify the first invalid step, and provide the correction.
For a prism net with edges 2,7,2 cm, a student writes Step 1: face-type areas (14, 4, 14). Step 2: total area 32 cm², counting one of each type. Locate the first invalid step and correct it.