Geometry desk
Triangle Area Calculator
Calculate a triangle's area from its base and perpendicular height.
Triangle Area Calculator: Measure a triangle's enclosed surface when you know a base and the perpendicular distance from that base to the opposite vertex. The result applies to acute, right and obtuse triangles, provided the height belongs to the base you enter. Runs 100% locally in your browser with zero server file uploads.
- Category
- Calculators
- Runs
- In your browser
- Cost
- Free · no sign-up
- Availability
- Ready to use
Area
30 cm²
Area = (base × height) ÷ 2- Height must be perpendicular to the chosen base.
- Dimensions are measured in the same unit.
- Values must be finite and greater than zero.
Formula and worked example
Area = (base × height) ÷ 2
A worked example with sample values:
| Inputs | |
|---|---|
| Base | 10 cm |
| Height | 6 cm |
| Results | |
|---|---|
| Area | 30 cm² |
Why base times height is halved
Use b for the chosen base, h for its perpendicular height and A for area. A = b × h ÷ 2. Place two identical triangles together along a suitable side to form a parallelogram. Its area is b × h, and each triangle contributes half. Sliding the top vertex parallel to the base changes the outline but leaves b, h and the area unchanged.
For a base of 10 cm and height of 6 cm, multiply 10 × 6 = 60 cm², then halve: A = 60 ÷ 2 = 30 cm². The displayed Area = 30 cm². A triangle with this base and height need not have either of its other sides equal to 6 cm.
The triangle area rule in OpenStax (https://openstax.org/books/prealgebra-2e/pages/9-4-use-properties-of-rectangles-triangles-and-trapezoids) is based on the perpendicular altitude. Choose a base you can measure reliably.
Recovering an altitude and checking units
Rearranging the area equation gives h = 2A ÷ b. If the area is 30 cm² and the base is 10 cm, the height is 2 × 30 ÷ 10 = 6 cm. The square unit divided by a length returns a length, which is a useful check on the rearrangement. Entering base in centimetres and altitude in millimetres would mix scales: convert first. For an answer in m², divide a cm² result by 10,000. The tool requires a non-zero base and height; collinear vertices have zero area and are excluded.
How to use it
- Enter positive dimensions in the same unit.
- Choose the unit used for every dimension.
- Calculate, then review the result and formula.
Privacy & limitations
Every value and calculation stays in your browser. No dimensions are uploaded or sent to an external service.
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Frequently asked questions
Can this triangle calculator use three side lengths?
This form takes base and perpendicular height only. It does not offer Heron's formula or three side fields. If only sides are known, obtain the matching altitude separately before using this tool.
Where is the height of an obtuse triangle?
Draw a line at a right angle from the opposite vertex to the line containing the base. The foot may lie outside the triangle, on an extension of the base. That outside altitude is still the correct height.
Is a sloping triangle side the same as its height?
Usually no. A height must meet the chosen base at 90°. A side can serve as height only when it is perpendicular to that base, as with the two legs of a right triangle. An inclined side overstates the height.
Embed this tool
Free to use on any website. Paste the code where the tool should appear; the link under it lets readers open the full page.
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<p style="margin:4px 0 16px;font-size:13px"><a href="https://toea.com/triangle-area-calculator">Triangle Area Calculator</a> · TOEA</p>
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