Triangle area using base and perpendicular height
Two matching triangles can form a parallelogram with the same base and height. One triangle occupies half that area, which explains the factor of one half.
What the formula is saying
Multiply base b by the perpendicular height h, then divide by two. The height meets the base, or its extended line, at a right angle.
Read the symbols in plain language
- b
- Base lengthm
- h
- Perpendicular heightm
Sort out the units first
Both lengths here use metres, so area is m². A sloping side is not the height unless it is perpendicular to the chosen base.
Let’s solve one together
Read the given values, follow each operation, then check what the result means.
- b · Base length
- 6 m
- h · Perpendicular height
- 4 m
Find the corresponding parallelogram area
The base–height product gives a full parallelogram.
(6) × (4) = 24 m²Take half
One of the two matching triangles occupies half the area.
(24) ÷ 2 = 12 m²
Does this worked answer make sense?
The result is half of 6 × 4 = 24 m², so 12 m². Different base-height pairs can give the same area.
Now try your own values
Change a value or its unit. The same method will show your calculation, step by step.
Results update only when you calculate. The lesson example above stays unchanged.
Your turn — check your understanding
Use these new values. Work it out first, then check your answer.
- b · Base length
- 8 m
- h · Perpendicular height
- 5 m
Find: Triangle area using base and perpendicular height
A hint, not the answer
Multiply base b by the perpendicular height h, then divide by two. The height meets the base, or its extended line, at a right angle.
Both lengths here use metres, so area is m². A sloping side is not the height unless it is perpendicular to the chosen base.
Show the full practice solution
Compare the steps with your work; revealing a solution does not mark the lesson complete.
Find the corresponding parallelogram area
The base–height product gives a full parallelogram.
(8) × (5) = 40 m²Take half
One of the two matching triangles occupies half the area.
(40) ÷ 2 = 20 m²
Avoid the common trap
Using an oblique side as height gives a wrong area. Forgetting to halve gives twice the triangle area.
When this method applies — and when it does not
Any planar triangle when a base and its true perpendicular height are known. Three side lengths alone require another method, such as Heron’s formula.
One idea understood. Keep going.
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Sources & further reading
References open in a new tab and explain the underlying principles. The teaching text and examples here are SimpleFlick’s own; the source organisations have not endorsed this calculator.
Lesson updated: · Worked examples checked against the implemented formula; not an independent engineering certification.