Learn with Amar
Teaching video
A teaching recording for this chapter has not been published yet. Start with the worked example below and explore the related animations where available.
Grade 7 chapters and video availability01 · Read and understand
What you will learn
- Explain how to count all faces in a rectangular box.
- Solve the two practice problems and explain how the assumptions affect the answers.
Before you start
Rectangle area and equal opposite faces.
Keep paper nearby. Read the question once for the context, then again to identify what is known and what you need to find.
Start with a question
A closed rectangular box measures 5 cm by 3 cm by 2 cm. How much surface area does it have?
Why this math matters
Surface area measures covering and requires adding the areas of the exposed faces. Draw a net and mark excluded faces when estimating the covering area of packaging.
Set up the model
A useful answer starts with clear assumptions:
- The box is closed and all six faces count.
- Material thickness and overlaps are ignored.
02 · Work through the example
Follow the reasoning, one step at a time.
Try to predict the next step before reading it. After each calculation, explain why the operation makes sense and how it helps answer the original question.
Work through it with Amar
See this example unfold.
The complete worked example, one idea at a time.
Count all faces in a rectangular box
PausedQuestion: Start with the question. Paused.
Question
Start with the question
A closed rectangular box measures 5 cm by 3 cm by 2 cm. How much surface area does it have?
Before you calculate
Read what is known and what you need to find. Make a prediction before moving to the first calculation.
Starts paused. Play advances through the full text at a reading pace; pause whenever you need more time. Previous, Next, and the phase buttons let you set your own pace. Playback pauses when this walkthrough leaves the screen or you switch tabs.
Your device’s reduced-motion setting keeps each phase still. Manual controls remain available. The full written solution stays below.
Represent the quantities
face areas: 5×3 = 15; 5×2 = 10; 3×2 = 6 cm²
There are three different face sizes.
Apply the relationship
surface area = 2(15 + 10 + 6)
Every rectangular face has an equal opposite partner.
Check and interpret
surface area = 62 cm²
This is the exterior covering, not the interior capacity.
The result
surface area = 62 cm²
This is the exterior covering, not the interior capacity.
Common mistakes to catch
- Multiplying length, width, and height gives volume, not surface area.
- An open container has fewer exposed faces than a closed box.
03 · Practice independently
Try it before revealing the answer.
Use paper or a calculator as needed. Write your units and reasoning, then open the hint or explanation to check your approach.
Practice 1
A cube has edge length 4 cm. Find its surface area.
Show a hint
There are six equal square faces.
Reveal answer and explanation
96 cm²
6(4²) = 6(16) = 96.
Practice 2
Remove the 5 cm by 3 cm lid from the original box. What area remains?
Show a hint
Remove only one face from 62.
Reveal answer and explanation
47 cm²
62 − 15 = 47; the bottom still counts.
Take the idea with you
Draw a net and mark excluded faces when estimating the covering area of packaging.
04 · Reflect and continue
Can you explain it in your own words?
Before moving on, explain the main idea without looking at the worked example. Try both practice questions, check your reasoning, and name one mistake you now know how to avoid. Return to a step if you still need support.
Up next: Build an equation from triangle angles
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