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.
Browse grades and teaching videos01 · Read and understand
What you will learn
- Convert metres to centimetres.
- Add all four sides of a rectangle.
- Distinguish length units from area units.
Before you start
Addition, multiplication by 100, and recognizing a rectangle.
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 rectangular display is 1.2 m wide and 80 cm tall. What length of border follows all four edges, with no overlap or gaps?
Why this math matters
Measurements become useful only when their units agree. A display border follows a line around the outside, while paper covering the display fills a surface. Drawing the shape first helps you choose which quantity the question actually asks for.
Set up the model
A useful answer starts with clear assumptions:
- The display has four straight sides and four right angles.
- Opposite sides have equal lengths, and the stated measurements are exact for this exercise.
- The border has negligible width; cutting loss and joins are excluded.
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.
Measure a display before finding its border
PausedQuestion: Start with the question. Paused.
Question
Start with the question
A rectangular display is 1.2 m wide and 80 cm tall. What length of border follows all four edges, with no overlap or gaps?
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.
Choose one unit
1.2 m × 100 cm/m = 120 cm
The metre units cancel. Converting the width keeps both dimensions in centimetres before any addition.
Label every edge
120 cm, 80 cm, 120 cm, 80 cm
The opposite edges of a rectangle match. Walking once around the display includes each edge exactly once.
Add and convert back
P = 120 + 80 + 120 + 80 = 400 cm = 4 m
The answer is a length. Multiplying 120 by 80 instead would calculate the area of the face.
The result
The ideal border length is 4 m.
This is the geometric distance around the rectangle, not a purchasing quantity with allowance. A label of 4 m² would describe a different kind of quantity and cannot answer this border question.
Common mistakes to catch
- Adding 1.2 and 80 without converting combines unlike units.
- Adding only width and height counts half the border.
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 rectangular card is 30 cm by 0.2 m. Find its perimeter.
Show a hint
Convert 0.2 m first.
Reveal answer and explanation
100 cm, or 1 m
The height is 20 cm, so P = 2(30 + 20) = 100 cm.
Practice 2
A rectangle has perimeter 3 m and width 90 cm. Find its height.
Show a hint
Use 300 = 2(90 + h).
Reveal answer and explanation
60 cm
Half the perimeter is 150 cm; subtracting the width leaves 60 cm.
Take the idea with you
Before measuring a frame, edge strip, or drawing, write whether you need a length, a surface area, or a volume.
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: Find a triangular panel's missing angles
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