Geometry
Area from base and height — or from three sides with Heron's formula — with the perimeter alongside.
All lengths in the same unit. Results update as you type. All calculations run locally in your browser.
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From base and height: area = ½ × base × height. From three sides a, b, c: first the semiperimeter s = (a + b + c) ÷ 2, then Heron's formula, area = √(s(s − a)(s − b)(s − c)). The two methods agree whenever the height matches the sides; they are independent checks on each other. The three sides must satisfy the triangle inequality — each side shorter than the sum of the other two — or no triangle exists.
Base 10 and height 6: area = ½ × 10 × 6 = 30. For the 3–4–5 triangle: s = (3 + 4 + 5) ÷ 2 = 6, so area = √(6 × 3 × 2 × 1) = √36 = 6, and the perimeter is 3 + 4 + 5 = 12. The 3–4–5 triangle is right-angled (3² + 4² = 5²), so its area also equals ½ × 3 × 4 = 6 — a third way to the same answer.
This page computes area only; it does not find missing sides or angles (a right triangle's sides and angles are covered by the right triangle calculator). Heron's formula needs all three sides and a valid triangle: if any side is zero or negative, or the triangle inequality fails, the page says so instead of showing a square root of a negative number. Results are in square units of whatever length unit you entered — the page does not convert units.
Because a triangle is half of a parallelogram with the same base and height: two copies of the triangle make the parallelogram, whose area is base × height. Halving gives the triangle.
When you know three sides but no height — for example, a plot of land measured along its three boundaries. If you know a base and its height, the simpler formula is enough.
Half the perimeter: s = (a + b + c) ÷ 2. Heron discovered that the area depends only on s and how far each side falls short of it. For 3–4–5, s = 6, and the shortfalls are 3, 2, and 1.
Then the triangle inequality fails — for example sides 1, 2, and 10, where 1 + 2 is less than 10. No such triangle exists, and the page reports that instead of a meaningless number.
For a genuine triangle, yes, provided the height belongs to the base you entered. If base-height area and Heron area disagree, one of the inputs is inconsistent — usually a height measured to the wrong base.
Yes: acute, right, obtuse, isosceles, and equilateral all use the same two formulas. Equilateral triangles have a shortcut (area = √3 ÷ 4 × side²), but Heron's formula gives the same result.
Results are estimates only and do not constitute professional advice.