Learn with Amar
Teaching video
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Grade 6 chapters and video availability01 · Read and understand
What you will learn
- Derive trapezoid area by pairing congruent copies.
- Explain your method and check what the result means in the stated situation.
Before you start
Fraction and decimal operations, whole-number factors, measurement units, and reading simple tables.
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 trapezoid has parallel sides 8 cm and 14 cm with perpendicular separation 5 cm. Find its area.
Why this math matters
Derive a new area formula by joining copies into a familiar shape. The worked example shows how to connect the situation, its mathematical representation, and a check on the result.
Set up the model
A useful answer starts with clear assumptions:
- Use the units, grouping rules, and reference whole stated in the question.
- Treat the supplied counts and measurements as exact within the classroom model, unless an estimate or a random outcome is requested.
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.
Average the parallel sides of a trapezoid
PausedQuestion: Start with the question. Paused.
Question
Start with the question
A trapezoid has parallel sides 8 cm and 14 cm with perpendicular separation 5 cm. Find its area.
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 situation
Pair two copies to make a parallelogram
Its base is the sum of the two parallel sides.
Connect the parts
Double area = (8 + 14) × 5 = 110 cm²
The paired figure retains the same perpendicular height.
State and check the result
Area = 110/2 = 55 cm²
Equivalently use average base length eleven times height five.
The result
Area = 110/2 = 55 cm²
Equivalently use average base length eleven times height five.
Common mistakes to catch
- Use the pair of parallel sides as the bases.
- The height is their perpendicular separation.
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
Find area for parallel sides 4 m and 10 m, height 3 m.
Show a hint
Average the bases, then multiply by height.
Reveal answer and explanation
21 m²
(4 + 10)/2 × 3 = 21.
Practice 2
Can the two sloping sides replace the parallel sides in this formula?
Show a hint
The pairing argument uses the parallel edges.
Reveal answer and explanation
No
Those lengths do not generally form the paired parallelogram's base.
Take the idea with you
Derive a new area formula by joining copies into a familiar shape.
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: Count every face in surface area
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