How this calculator works
The base altitude bisects both the base and the apex angle. This produces two right triangles with hypotenuse a, horizontal leg b/2 and vertical leg h. A length alone cannot set the shape; a second independent measurement is required. The tool also reports the altitude to either equal leg, which is generally different from the base altitude.
Formula
h² = a² - (b/2)²; b = 2a sin(B/2); K = bh/2; P = 2a+b; A = C = (180°-B)/2; R = a²b/(4K); r = 2K/P.
Worked example
Equal legs of 5 m and base 6 m give h = 4 m, area 12 m², perimeter 16 m, inradius 1.5 m and circumradius 3.125 m.
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Frequently asked questions
Can the base be longer than a leg?
Yes. It must be shorter than twice a leg. A base equal to twice a leg makes a flat triangle.
Can the apex angle be obtuse?
Yes. The apex angle can be anywhere strictly between 0° and 180°. Each base angle must be acute.
Does this include equilateral triangles?
Yes. When the base equals a leg, all three angles are 60°. The equilateral tool is simpler if that is already known.