The lesson
Read each section in order, work through every example on paper, then use the practice problems and quick check at the bottom.
What a net is
A net is a 3-D shape unfolded so all its faces lie flat. Surface area is the total area of all those faces added together.
Surface area of a cube
A cube has 6 identical square faces. Find the area of one face, then multiply by 6.
Area measures how much space a flat shape covers, in square units. Picture tiles on a floor. Each tile is one square unit.
Break complicated shapes into rectangles or triangles you already know how to measure, then add the pieces together.
Find the surface area of a cube with edge 4 cm.
- 1One face: 4 × 4 = 16 cm².
- 2Six faces: 6 × 16 = 96 cm².
Why this matters
Unfold a solid into a flat net and add up every face.
These ideas show up on homework, quizzes, and the next unit in this grade. Getting comfortable here saves time later when the problems stack more steps together.
Common mistakes to avoid
Rushing to the answer without writing steps. Clear work helps you catch mistakes and shows your reasoning.
Re-reading the question too quickly. Underline what you are solving for before you start calculating.
Key ideas from this lesson
- What a net is
- Surface area of a cube
Video walkthroughs
Surface Area Using Nets
Add face areas after unfolding prisms and pyramids.
Watch on YouTube
Practice
For each problem: write your work in the box, type your answer, and check it. If you are stuck, reveal the solution one step at a time. Do not skip straight to the final answer.
Exercise 1
Try it yourselfA cube has edge 3 cm. Find the area of one face and the total surface area.
Step-by-step solution
- 1One face: 3 × 3 = 9 cm².
- 2Six faces: 6 × 9 = 54 cm².
Exercise 2
Try it yourselfA rectangular prism has faces 4×3, 4×2, and 3×2 cm. Find the surface area.
Step-by-step solution
- 1Areas: 12, 8, and 6 cm².
- 2Each appears twice: 2(12+8+6) = 2(26) = 52 cm².
Exercise 3
Try it yourselfFind the surface area of a cube with edge 5 in.
Step-by-step solution
- 1One face: 25 in².
- 2Six faces: 6 × 25 = 150 in².
Exercise 4
Try it yourselfAn open box (no top) is 10 cm × 6 cm × 4 cm. How much cardboard is needed?
Step-by-step solution
- 1Bottom: 10 × 6 = 60.
- 2Four sides: 2(10×4) + 2(6×4) = 80 + 48 = 128.
- 3Total: 60 + 128 = 188 cm².
Exercise 5
Try it yourselfA room needs paint on four walls only (no ceiling or floor). Walls are 12 ft × 8 ft (two) and 10 ft × 8 ft (two). Find the painted area.
Step-by-step solution
- 112×8 walls: 2 × 96 = 192 ft².
- 210×8 walls: 2 × 80 = 160 ft².
- 3Total: 192 + 160 = 352 ft².
Quick check
Answer all questions. Retake the quiz until you feel confident before moving on.
Nets & Surface Area
Question 1 of 4
Surface area of a rectangular prism equals the area of all 6 faces added together.