Calculate triangle area from base and height, three sides, two sides and an included angle, or coordinates.
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Also in Triangles
Triangle Geometry
The triangle area calculator finds the area of a triangle using several common input methods — base and height, three side lengths, two sides with the included angle, or vertex coordinates. Each method suits different situations depending on the information you have.
The most familiar formula is half the base times the height. The height must be the perpendicular distance from the base to the opposite vertex, not a slant measurement. This method is ideal when one side and a measured altitude are known.
Area = (1/2) * base * height
The base can be any side as long as the height is measured perpendicular to that side.
When all three side lengths are known but no height is available, Heron's formula computes the area through the semi-perimeter. It is particularly useful in surveying and construction where side distances are measured directly.
Area = sqrt(s(s-a)(s-b)(s-c)), s = (a+b+c)/2
The semi-perimeter s is half the perimeter; a, b, c are the three side lengths.
When two sides and the angle between them are known, the area equals half the product of the two sides times the sine of the included angle. This method avoids the need to find a height separately.
Area = (1/2) * a * b * sin(C)
C is the angle between sides a and b.
Frequently asked questions
Use Heron's formula: compute the semi-perimeter s = (a+b+c)/2, then Area = sqrt(s(s-a)(s-b)(s-c)).
No. Any side can serve as the base; the height is simply the perpendicular distance from that side to the opposite vertex.
Yes. Use the shoelace formula with the three vertex coordinates: Area = |x1(y2-y3) + x2(y3-y1) + x3(y1-y2)| / 2.
Related
These related calculators come from the same leaf category, nearby sibling categories, or the same top-level topic.
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Calculate the area, perimeter, height, inradius, and circumradius of an equilateral triangle from its side length.
