A 10-second estimate catches impossible answers before they cost marks.
Key formulas
Rough sizes
If a triangle sits inside a 6-by-8 rectangle, its area is less than 48. An answer of 200 is already wrong.
Angle ballpark
A clearly acute corner cannot come out as 140° unless you chose the wrong triangle.
Make it a habit
Write a one-line estimate in the margin. Compare after the exact value appears.
Worked example
Worked example
Problem. A triangle is drawn inside a 6 cm by 8 cm rectangle. A student gets area 200 cm². Is this believable?
Solution. The rectangle area is 48 cm², so any triangle inside has area < 48. An answer of 200 is impossible — recheck the calculation.
Volume
A cone inside a cylinder of volume 90 should have volume under 90 — usually about a third if dimensions match.
Review quiz
Triangle inside a 5×9 rectangle. Which area is impossible?
Practice questions
- Give an upper bound for the area of a triangle inside a 5×9 rectangle.
- What estimate would you write for tan of a very small angle?
Study notes
Does estimating waste time?
Ten seconds can save five minutes of searching for a sign error.