Area
Compare the areas of triangles, rectangles and composite figures. Then change their dimensions to test what matters.
Base and height
1 comparison · No time limit · Explore after checking
Example
Example
Compare the triangle’s area with the stated area.
Review the comparison
The triangle has base 5 units and perpendicular height 4 units.
Its apex may move along a line parallel to the base.
The base and perpendicular height stay fixed; the apex can slide.
Area of the triangle
12.5 square units
Choose an answer to try the example.
Why?
Explore the relationship
Place the perpendicular height outside the triangle without changing its area.
In this drawing
Need a clue?
The height can meet an extension of the base. Move the apex beyond either endpoint.
Example positions
Slide the apex, including outside the base. Watch which measurements stay fixed.
The controls preserve the givens. Examples illustrate the rule; the explanation proves it.
Go further Apply the idea
Further practice does not change your comparison score.
Continue your unfinished round
Your answers are saved in this tab. Continue from where you left off.
Continuing uses no additional practice start.
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Starting the new round uses one practice start.
- Answered
- 0 / 1
- Active time
- 0:00
Round complete.
Optional and off by default. Share starts, completions, replays and error categories. For visits from ChatGPT, starts and completions can also include the first QuickenBrain page and broad country. No answers, drawings or names.
How this data is usedHelp
Choose whether Quantity A is greater, Quantity B is greater, the quantities are equal, or the relationship cannot be determined. Use only the stated givens. A drawing shows one possible case.
Your first checked answer counts. A shown answer counts as 0 correct. A checked comparison is saved immediately, so you can explore afterward without losing your result. An unfinished comparison is not saved as a result.
After checking, use the controls to solve an exploration goal. When the relationship cannot be determined, save two valid cases with different comparisons. Open Go further to apply the idea to a new question. These activities are optional and do not change your score.
Angles and trigonometric functions use degrees. Levels increase the mathematical complexity; they do not measure IQ.
About this practice
Learn a method
Use base and heightCompare the areas of triangles, rectangles and composite figures. Then change their dimensions to test what matters.
For a broader mix of practices, explore the geometry practice test. Membership is required to start a test.
Report a problem
Optional and off by default. Share starts, completions, replays and error categories. For visits from ChatGPT, starts and completions can also include the first QuickenBrain page and broad country. No answers, drawings or names.
How this data is used