A focused Grade 7 learning session for Surface Area of Three-Dimensional Objects using visual models, worked examples, strategy guidance, and a short mastery check.
Student goal: I can solve problems involving surface area of three-dimensional objects.
Surface Area of Three-Dimensional Objects is part of Grade 7 Measurement Geometry. This activity focuses on the central idea students need before they move into independent practice.
Students will build Grade 7 mastery of surface area of three-dimensional objects using models, equations, and test-style reasoning.
| What to notice | How to use it |
|---|---|
| Numbers, units, labels, diagrams, or graphs | Identify what each part represents before calculating. |
| The relationship in the problem | Connect the model to an equation, comparison, or explanation. |
Use the figures and worked questions in the practice set below as the visual model for this skill.
Read the first practice question slowly. Decide what the question is asking, choose a strategy, solve, and then compare your reasoning with the answer explanation.
For Surface Area of Three-Dimensional Objects, a strong worked example should show the setup, the calculation or model, and a final answer that matches the context.
Many Grade 7 test questions use real situations. Look for quantities, units, rates, measures, expressions, or data values that connect the math to the story.
After solving, explain what the answer means in the situation, not just the number you calculated.
I can solve problems involving surface area of three-dimensional objects.
Use the warmup, guided question, practice set, and exit questions below to check whether this skill is ready or needs more practice.
Use scratch paper. The explanation matters more than simply seeing whether the choice is correct.
A rectangular prism has length \(4\) cm, width \(3\) cm, and height \(5\) cm. What is its surface area?
Answer C: \(94\) cm\(^2\)
\(SA=2(lw+lh+wh)=2(4\cdot3+4\cdot5+3\cdot5)=2(12+20+15)=2(47)=94\) cm\(^2\).
A cube has edge length \(6\) cm. Find its surface area.
Answer D: \(216\) cm\(^2\)
A cube has 6 faces, each a square with side length \(6\) cm. \(SA = 6s^2 = 6(6)^2 = 6(36) = 216\) cm\(^2\).
A rectangular prism with dimensions \(5\) m \(\times\) \(3\) m \(\times\) \(2\) m is shown above. Calculate its surface area.
Answer B: \(62\) m\(^2\)
\(SA = 2(5 \cdot 3 + 5 \cdot 2 + 3 \cdot 2) = 2(15 + 10 + 6) = 2(31) = 62\) m\(^2\).
A rectangular prism has length \(7\) cm, width \(2\) cm, and height \(4\) cm. What is the total surface area?
Answer C: \(100\) cm\(^2\)
\(SA = 2(lw + lh + wh) = 2(7 \cdot 2 + 7 \cdot 4 + 2 \cdot 4) = 2(14 + 28 + 8) = 2(50) = 100\) cm\(^2\).
A cube has surface area \(150\) cm\(^2\). What is the edge length of the cube?
Answer A: \(5\) cm
If \(SA = 6s^2 = 150\), then \(s^2 = 25\), so \(s = 5\) cm.
The rectangular prism shown has dimensions \(3\) in \(\times\) \(2\) in \(\times\) \(4\) in. What is its surface area?
Answer B: \(52\) in\(^2\)
\(SA = 2(3 \cdot 2 + 3 \cdot 4 + 2 \cdot 4) = 2(6 + 12 + 8) = 2(26) = 52\) in\(^2\).
A cube has edge length \(4\) cm. What is the total surface area?
Answer C: \(96\) cm\(^2\)
\(SA = 6s^2 = 6(4)^2 = 6(16) = 96\) cm\(^2\).
A triangular prism has a right triangular base with legs \(3\) ft and \(4\) ft (hypotenuse \(5\) ft), and the prism has depth \(3\) ft. Find the surface area.
Answer C: \(48\) ft\(^2\)
Two triangular bases: \(2 \times \frac{1}{2}(3)(4) = 12\) ft\(^2\). Three rectangular sides: \(3 \times 3 = 9\), \(4 \times 3 = 12\), \(5 \times 3 = 15\) ft\(^2\). Total: \(12 + (9 + 12 + 15) = 12 + 36 = 48\) ft\(^2\).
A rectangular prism has dimensions \(6\) cm \(\times\) \(4\) cm \(\times\) \(3\) cm. What is its surface area?
Answer B: \(108\) cm\(^2\)
\(SA = 2(6 \cdot 4 + 6 \cdot 3 + 4 \cdot 3) = 2(24 + 18 + 12) = 2(54) = 108\) cm\(^2\).
The net shown represents a rectangular prism. What is the surface area of the prism?
Answer C: \(190\) m\(^2\)
From the net with labeled edges \(5\) m, \(5\) m, and \(7\) m, the dimensions are \(5 \times 5 \times 7\). \(SA = 2(25) + 2(35) + 2(35) = 50 + 70 + 70 = 190\) m\(^2\).
A cube has edge length \(3\) cm. What is its surface area?
Answer D: \(54\) cm\(^2\)
\(SA = 6s^2 = 6(3)^2 = 6(9) = 54\) cm\(^2\).
