Triangle and circle calculations — area, perimeter, Pythagorean theorem, circumference, and more.
Area from base & height
Area = (base × height) / 2
12
Heron's formula (all three sides)
Area (Heron's)
6
Perimeter (a+b+c)
12
Frequently Asked Questions
Area = (base × height) / 2. The height must be perpendicular to the base. If you know all three sides, use Heron's formula: s = (a+b+c)/2, Area = √(s(s-a)(s-b)(s-c)).
For a right triangle: a² + b² = c², where c is the hypotenuse (longest side, opposite the 90° angle). Use it to find a missing side when two are known.
By sides: equilateral (all sides equal), isosceles (two sides equal), scalene (no sides equal). By angles: acute (all < 90°), right (one = 90°), obtuse (one > 90°). Angles always sum to 180°.
Area = πr², where r is the radius. If you know the diameter, r = d/2. Example: radius 5 → Area = π × 25 ≈ 78.54.
Circumference = 2πr = πd. Multiply the diameter by pi (≈ 3.14159). Example: radius 7 → circumference = 2 × π × 7 ≈ 43.98.
Rearrange Area = πr²: r = √(Area/π). Example: Area = 50 → r = √(50/π) ≈ 3.99.
Diameter = Circumference ÷ π. Since C = πd, rearranging gives d = C/π. Example: C = 25.13 → d ≈ 8.