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
- Interpret a 1:50 length ratio.
- Apply area scaling correctly.
- Redraw one object at another scale.
Before you start
Ratios, rectangular area, and centimetre-to-metre conversion.
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 room appears as 12 cm by 8 cm on a 1:50 drawing. Find its actual dimensions and area, then its drawing dimensions at 1:100.
Why this math matters
Changing a drawing's scale changes its picture, not the room. Lengths scale in one direction, while area scales in two directions simultaneously.
Set up the model
A useful answer starts with clear assumptions:
- The drawing has not been resized after its scale was specified.
- The room is rectangular and every length uses the same scale.
- Drawing dimensions are exact for this calculation.
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.
Read a scale drawing without scaling area incorrectly
PausedQuestion: Start with the question. Paused.
Question
Start with the question
A rectangular room appears as 12 cm by 8 cm on a 1:50 drawing. Find its actual dimensions and area, then its drawing dimensions at 1:100.
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.
Scale the lengths
12 × 50 = 600 cm = 6 m; 8 × 50 = 400 cm = 4 m
One drawing centimetre represents fifty real centimetres. Convert the resulting lengths before calculating square metres.
Find and check area
A = 6 × 4 = 24 m²
The drawing area is 96 cm². Multiplying by 50² gives 240,000 cm², also 24 m².
Use the new scale
600/100 = 6 cm; 400/100 = 4 cm
The new drawing is half as wide and half as tall. Its paper area becomes one quarter of the previous drawing's area.
The result
The room is 6 m by 4 m, with area 24 m²; its 1:100 drawing is 6 cm by 4 cm.
The factor 50 applies to lengths. Applying it only once to area misses scaling in the second direction.
Common mistakes to catch
- A screenshot or print resize can invalidate a written scale.
- One square metre is 10,000 square centimetres, not 100.
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
At 1:20, a segment is 7 cm long. Find its real length.
Show a hint
Multiply by 20.
Reveal answer and explanation
1.4 m
7 × 20 = 140 cm = 1.4 m.
Practice 2
A similar shape triples every length. How does its area change?
Show a hint
Scale in two directions.
Reveal answer and explanation
It becomes 9 times as large.
The area multiplier is 3², regardless of the original area.
Take the idea with you
Check whether a ratio applies to length, area, or volume before using a model's scale.
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 straight route and its halfway point
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