The classic base-times-height-over-two formula, on a focused single-shape page.
How it works
Multiplying the base by the perpendicular height and dividing by 2 gives the area.
What this does not include
This does not include other shapes — for a multi-shape tool covering rectangles, circles, trapezoids and more, use this site’s general area calculator instead.
How to use this calculator
- Enter the base and the perpendicular height.
A worked example
Base 10, height 6 → area = (10 × 6) ÷ 2 = 30. Base 7, height 4 → area = (7 × 4) ÷ 2 = 14.
What the variables mean
| Variable | Meaning |
|---|---|
| Base | Any one side, chosen as the reference |
| Height | The perpendicular (straight-up) distance from that base to the opposite vertex |
Edge cases worth knowing
A slanted side is not the height — using a triangle’s slanted side instead of the true perpendicular distance overstates the area, since the perpendicular distance is always the shortest path from the base to the opposite vertex.
The formula works for any triangle, not just right triangles, as long as the height used is genuinely perpendicular to the chosen base — obtuse triangles sometimes need that perpendicular line extended outside the triangle itself to measure it.
Frequently asked questions
What does “perpendicular height” mean?
The straight-up distance from the base to the opposite vertex, at a right angle — not the length of a slanted side, which would overstate the area if used instead.
Why divide by 2?
A triangle is exactly half of the parallelogram formed by the same base and height, so its area is half of base times height.
Does this work for any triangle shape?
Yes — as long as the correct perpendicular height for the chosen base is used, this formula works for any triangle, not just right triangles.
