📏 Surface Area & Nets
Net = unfolded 3D shape
▶ Play Door 6Nets of 3D Shapes
What is a Net?
A net is a 2-dimensional diagram that can be folded to form a 3-dimensional shape. Think of it as the "pattern" or "unfolded" version of a solid.
Common Nets:
3D ShapeNet DescriptionRectangular Prism6 rectangles (2 pairs of equal faces)Cube6 identical squaresTriangular Prism2 triangles + 3 rectanglesSquare Pyramid1 square + 4 trianglesTriangular Pyramid (Tetrahedron)4 trianglesDrawing Nets Tips:
• Identify all faces of the 3D shape
• Arrange faces so they connect along edges
• Make sure net can fold without overlap
Worked example
Problem: How many faces does a net of a rectangular prism have? What shapes are they?
- Rectangular prism has 6 faces
- All faces are rectangles (could include squares)
- Answer: 6 rectangles
Answer: Answer: 6 rectangles
Calculating Total Surface Area from Net
What is Surface Area?
Surface area is the total area of all faces of a 3D shape. It's like the amount of wrapping paper needed to cover the entire shape.
Method 1: Using a Net
• Draw or visualize the net
• Find area of each face
• Add all areas together
Method 2: Using a Formula
ShapeSurface Area FormulaRectangular PrismSA = 2(lw + lh + wh)CubeSA = 6s²Triangular PrismSA = bh + 2ls + lw (varies)Square PyramidSA = s² + 2slNote: "l" = length, "w" = width, "h" = height, "s" = side