6.G.4: Nets and Surface Area
Also written as 6.G.A.4 and CCSS.MATH.CONTENT.6.G.A.4 · Cluster: Solve real-world and mathematical problems involving area, surface area, and volume.
The Official Wording
Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.
Common Core State Standards, Grade 6, Geometry · Read it at the source · Checked October 14, 2026
What 6.G.4 Means in Plain English
Sixth graders unfold a box or a triangular prism into its net, a flat pattern of rectangles and triangles, and add the area of every piece. A 10 cm prism with 3-4-5 triangle ends unfolds into two 6 cm² triangles and rectangles of 30, 40 and 50 cm².
Surface area answers wrapping-paper and paint questions: how much material covers the outside. It also separates the two measurements of a solid, the skin in square units and the filling in cubic units (6.G.2). In 7th grade the same nets handle pyramids and composite solids (7.G.6).
6.G.4 I Can Statements
- I can draw the net of a rectangular or triangular prism.
- I can match each face of a net to the solid it came from.
- I can add the areas of a net to find surface area.
6.G.4 Worked Example
A triangular cheese box unfolded into five faces, each one measured and added, then checked by grouping the rectangles.
A cheese box is a triangular prism. Its ends are right triangles with sides 3 cm, 4 cm and 5 cm, and the box is 10 cm long. How much cardboard does it take?
- Unfold it in your head: the net is the two triangular ends and three rectangles, one for each edge of the triangle, all 10 cm long.2 triangles + 3 rectangles: 10 × 3, 10 × 4, 10 × 5
- The ends are right triangles with legs 3 and 4.2 × (½ × 3 × 4) = 2 × 6 = 12 cm²
- Each rectangle is 10 cm long and as wide as the triangle edge it folds up from.10 × 3 + 10 × 4 + 10 × 5 = 30 + 40 + 50 = 120 cm²
- Surface area is every face of the net added together.12 + 120 = 132 cm²
Check it: Count faces on the net: 5 pieces, 2 triangles and 3 rectangles, each with a number. The three rectangles together are 10 × (3 + 4 + 5) = 10 × 12 = 120, the same 120.
Common Mistakes with 6.G.4
Missing a face
Only the three rectangles: 30 + 40 + 50 = 120 cm²
Try this: Have students number the faces on the solid, then on the net, and tick each one off as its area goes into the sum.
Using the wrong width for a rectangle
All three rectangles 10 × 4: 3 × 40 = 120
Try this: Fold the net up and show that each rectangle meets a different edge of the triangle, so their widths are 3, 4 and 5.
Cubic units on a flat net
132 cm³
Try this: Point at the net: it is flat, so it is measured in square centimeters. Cubic units belong to the filling, which is 6.G.2.
Where 6.G.4 Fits
Practice 6.G.4
Quick Check
- A cube has edges of 4 cm. What is its surface area?
- A box is 5 in by 3 in by 2 in. How much paper covers it?
- A square pyramid has a 6 cm by 6 cm base and four triangular faces, each 5 cm tall. What is its surface area?