Given only the base and the length of the two equal sides, this finds the triangle’s height and area.
How it works
The perpendicular height is found using the Pythagorean theorem on half the base and the known leg length, then the standard base-times-height-over-two formula gives the area.
What this does not include
This does not include cases where the height is already known — for that simpler case, use this site’s triangle area calculator instead, which takes base and height directly.
How to use this calculator
- Enter the base and the length of the two equal sides.
A worked example
Base 6, equal-side (leg) length 5: height = √(5² − 3²) = √16 = 4. Area = (6 × 4) ÷ 2 = 12.
What the variables mean
| Variable | Meaning |
|---|---|
| Base | The unequal (third) side |
| Leg | Either of the two equal sides |
| Height (derived) | Found via the Pythagorean theorem from half the base and the leg |
Edge cases worth knowing
A leg shorter than or equal to half the base can’t form a real triangle — the two legs simply wouldn’t reach each other, so this calculator returns no result rather than an invalid height.
When the leg equals the base, the triangle becomes equilateral — the same formula still applies correctly, it’s just a special case of the general isosceles one.
Frequently asked questions
Why does the perpendicular height bisect the base exactly?
Because the two equal sides create a symmetric triangle, and the line from the apex straight down to the base must split it into two mirror-image right triangles.
What if the leg length is too short?
If a leg is shorter than or equal to half the base, the triangle can’t physically exist — the calculator declines to show a result rather than an invalid answer.
Is an equilateral triangle a special case of this?
Yes — when the leg length equals the base itself, the isosceles triangle becomes equilateral, and this same formula still applies correctly.
