Calculate triangle area, perimeter, angles, and sides. Solve any triangle using SSS, SAS, ASA, AAS, or SSA methods with step-by-step solutions.
Area
6.0000
square units
Perimeter
12.0000
units
Common triangle configurations
Side a
3.000000
Side b
4.000000
Side c
5.000000
Angle A
36.8699 deg
Angle B
53.1301 deg
Angle C
90.0000 deg
Area
6.000000
Perimeter
12.000000
Semi-perimeter
6.000000
Type
Scalene Right
Inradius (inscribed circle)
1.000000
Circumradius (circumscribed circle)
2.500000
Coordinates relative to vertex C at origin, with B along positive x-axis.
Intersection of medians
(1.0000, 1.3333)
Intersection of angle bisectors
(1.0000, 1.0000)
Intersection of perp. bisectors
(1.5000, 2.0000)
Intersection of altitudes
(0.0000, 0.0000)
Euler Line: In any non-equilateral triangle, the centroid (G), circumcenter (O), and orthocenter (H) are collinear, with G dividing OH in ratio 1:2.
Area Formulas:
Area = (1/2) x base x height
Area = (1/2) x a x b x sin(C)
Area = sqrt(s(s-a)(s-b)(s-c)) (Heron's formula)
Law of Cosines:
c^2 = a^2 + b^2 - 2ab*cos(C)
Used for: SSS (find angles), SAS (find third side)
Law of Sines:
a/sin(A) = b/sin(B) = c/sin(C)
Used for: ASA, AAS, SSA (with ambiguous case check)
Radii:
Inradius r = Area / s
Circumradius R = abc / (4 x Area)
3-4-5 Right Triangle
Sides: 3, 4, 5
Angles: 36.87 deg, 53.13 deg, 90 deg
Multiples work too: 6-8-10, 9-12-15
45-45-90 Triangle
Sides ratio: 1 : 1 : sqrt(2)
Isosceles right triangle
Example: 1, 1, 1.414...
30-60-90 Triangle
Sides ratio: 1 : sqrt(3) : 2
Half of equilateral triangle
Example: 1, 1.732, 2
Equilateral Triangle
All sides equal, all angles 60 deg
Area = (sqrt(3)/4) x side^2
Height = (sqrt(3)/2) x side
Area
6.0000
square units
Perimeter
12.0000
units
Triangle area = (base x height) / 2, or using Heron's formula: sqrt(s(s-a)(s-b)(s-c)) where s is semi-perimeter. The sum of interior angles always equals 180 degrees. Use Law of Sines (a/sinA = b/sinB = c/sinC) and Law of Cosines (c squared = a squared + b squared - 2ab cosC) to solve triangles.
A triangle is a polygon with three sides and three angles. The sum of interior angles is always 180 degrees. Triangles are classified by sides (equilateral, isosceles, scalene) and by angles (acute, right, obtuse). Triangle calculators use trigonometric laws to find unknown measurements from given values.
Test your understanding of triangle calculations
Practice with 6 problems to test your understanding.
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Triangle area = (base x height) / 2, or using Heron's formula: sqrt(s(s-a)(s-b)(s-c)) where s is semi-perimeter. The sum of interior angles always equals 180 degrees. Use Law of Sines (a/sinA = b/sinB = c/sinC) and Law of Cosines (c squared = a squared + b squared - 2ab cosC) to solve triangles.
For base and height: Area = (1/2) x base x height. For three sides (Heron's formula): s = (a+b+c)/2, Area = sqrt(s(s-a)(s-b)(s-c)). For two sides and included angle: Area = (1/2) x a x b x sin(C).
When you know two sides and an angle opposite to one of them (SSA), there may be zero, one, or two possible triangles. This happens because the sine function gives the same value for an angle and its supplement. Always check for the second solution!
c^2 = a^2 + b^2 - 2ab*cos(C). This generalizes Pythagorean theorem to any triangle. Use it to find a side when you know two sides and the included angle, or to find angles when you know all three sides.
a/sin(A) = b/sin(B) = c/sin(C). Each side divided by the sine of its opposite angle gives the same ratio. Use it when you know a side-angle pair plus one other measurement.
Centroid: intersection of medians (center of mass). Incenter: intersection of angle bisectors (center of inscribed circle). Circumcenter: intersection of perpendicular bisectors (center of circumscribed circle). Orthocenter: intersection of altitudes.
By sides: Equilateral (all equal), Isosceles (two equal), Scalene (none equal). By angles: Acute (all < 90 deg), Right (one = 90 deg), Obtuse (one > 90 deg). A triangle can be described by both, e.g., "Isosceles Right".
Last updated: 2025-01-15
Area
6.0000
square units
Perimeter
12.0000
units