Surface Area of 3D Shapes
Grade 6 · Math · Study Guide
Learn to find the surface area of rectangular prisms, triangular prisms, and pyramids by unfolding nets.
Surface area is the total area of all the faces (flat surfaces) of a 3D shape. Think of it as the amount of wrapping paper you'd need to cover a gift box exactly. The trick is to find the area of every face and add them all up.
A rectangular prism (like a cereal box) has 6 faces: top and bottom, front and back, left and right. Each pair of opposite faces is identical. The formula is SA = 2lw + 2lh + 2wh, where l is length, w is width, and h is height. For a box that is 4×3×2 cm: SA = 2(4×3) + 2(4×2) + 2(3×2) = 24 + 16 + 12 = 52 cm².
A net is a 2D shape that folds up into a 3D shape. Drawing a net helps you see all the faces clearly. For a cube with side length 5: all 6 faces are squares with area 25 each, so SA = 6 × 25 = 150 square units.
For a triangular prism, you have 2 triangular faces and 3 rectangular faces. Find the area of each triangle (½ × base × height) and each rectangle, then add them all. Units for surface area are always squared (cm², m², in²) because area is two-dimensional.
| Shape | Formula | Variables |
|---|---|---|
| Rectangular Prism | SA = 2lw + 2lh + 2wh | l=length, w=width, h=height |
| Cube | SA = 6s² | s=side length |
| Triangular Prism | SA = 2(½bh) + (P × l) | b=triangle base, h=triangle height, P=perimeter of triangle, l=prism length |
Key terms
- Surface Area
- The total area of all faces of a 3D shape, measured in square units
- Net
- A flat (2D) diagram that can be folded to form a 3D shape
- Face
- A flat surface on a 3D shape
- Rectangular Prism
- A 3D shape with 6 rectangular faces, like a box
Flashcards
- Surface area
- Total area of ALL faces of a 3D shape — measured in square units
- Rectangular prism SA formula
- SA = 2lw + 2lh + 2wh
- Cube SA formula
- SA = 6s² (6 identical square faces)
- Net
- A 2D unfolding of a 3D shape that shows all faces laid flat
- Units for surface area
- Always SQUARED: cm², m², ft², in²
- How many faces does a rectangular prism have?
- 6 — three pairs of congruent opposite faces
Practice questions
A rectangular prism has length 5 cm, width 3 cm, and height 4 cm. What is its surface area?
- 94 cm²
- 60 cm²
- 47 cm²
- 120 cm²
Show answer
Answer: 94 cm²
SA = 2(5×3) + 2(5×4) + 2(3×4) = 30 + 40 + 24 = 94 cm².
A cube has a side length of 6 in. What is its surface area?
- 216 in²
- 36 in²
- 216 in³
- 36 in³
Show answer
Answer: 216 in²
SA = 6s² = 6×36 = 216 in². (Not cubic — surface area uses square units.)
Surface area is measured in cubic units.
Show answer
Answer: False
Surface area is measured in SQUARE units (cm², in²). Cubic units are for volume.
A flat shape that can be folded into a 3D solid is called a ___.
Show answer
Answer: net
A net is the 2D unfolding that shows all faces of a 3D shape.
A rectangular prism has SA = 2(5×3) + 2(5×2) + 2(3×2). What is the surface area?
- 62 cm²
- 30 cm²
- 31 cm²
- 60 cm²
Show answer
Answer: 62 cm²
2(15) + 2(10) + 2(6) = 30 + 20 + 12 = 62 cm².
Fun facts
- Architects use surface area calculations to figure out how much paint, glass, or cladding material a building needs.
- A cube has less surface area relative to its volume than almost any other rectangular shape — that's why ice cubes are roughly cube-shaped to melt more slowly.
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