Learn with Amar
Teaching video
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Grade 7 chapters and video availability01 · Read and understand
What you will learn
- Explain how to find an L-shaped area by subtraction.
- Solve the two practice problems and explain how the assumptions affect the answers.
Before you start
Rectangle area and subtraction.
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
An L-shaped floor plan is a 9 m by 7 m rectangle with a 3 m by 2 m corner removed. What area remains?
Why this math matters
A composite region can be measured by combining simple nonoverlapping regions or subtracting a missing part. Sketch a decomposition and label any overlap before calculating the area of a complex plan.
Set up the model
A useful answer starts with clear assumptions:
- All corners are right angles.
- The removed rectangle lies completely inside one corner of the large rectangle.
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.
Find an L-shaped area by subtraction
PausedQuestion: Start with the question. Paused.
Question
Start with the question
An L-shaped floor plan is a 9 m by 7 m rectangle with a 3 m by 2 m corner removed. What area remains?
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
outer area = 9 × 7 = 63 m²
Start with the simple rectangle that encloses the whole plan.
Apply the relationship
removed area = 3 × 2 = 6 m²
The missing corner must use the same square-metre units.
Check and interpret
remaining area = 63 − 6 = 57 m²
Subtraction counts only the floor that remains.
The result
remaining area = 63 − 6 = 57 m²
Subtraction counts only the floor that remains.
Common mistakes to catch
- Adding component areas is valid only if overlap is handled.
- Subtracting side lengths alone does not find the missing rectangular area.
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 10 cm by 6 cm rectangle contains a 4 cm by 2 cm rectangular hole. Find the area outside the hole.
Show a hint
Subtract the inner rectangle's area.
Reveal answer and explanation
52 cm²
10(6) − 4(2) = 60 − 8 = 52.
Practice 2
Two rectangles of areas 18 and 12 cm² overlap by 5 cm². What is their combined area?
Show a hint
The overlap was counted in both rectangles.
Reveal answer and explanation
25 cm²
18 + 12 − 5 = 25; remove one duplicate count of the overlap.
Take the idea with you
Sketch a decomposition and label any overlap before calculating the area of a complex plan.
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: Extend a triangular area into a prism
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