Try this Drag the orange dots on each
vertex
to reshape the triangle. The formula shown will recalculate the area using this method.

Usually called the "side angle side" method, the area of a triangle is given by the formula below. Although
it uses the trigonometry Sine function, it works on any triangle, not just
right triangles.
*where*

a and b are the lengths of two sides of the triangle

C is the included angle (the angle between the two known sides)

ENTER TWO SIDES AND INCLUDED ANGLE | ||

Side 1 | clear | |

Side 2 | clear | |

Angle (degs) | clear | |

Area: | ||

Use the calculator above to calculate the area of a triangle given 2 sides and the angle between them.

In the figure above, the area would be given by the formula But we are not given h - the height. But we are given the side a and the angle C. We know that Transposing Substituting this into the top equation we get

If you know: | Use this |

Base and altitude | "Half base times height" method |

All 3 sides | Heron's Formula |

Two sides and included angle | Side-angle-side method |

x,y coordinates of the vertices |
Area of a triangle- by formula (Coordinate Geometry) Area of a triangle - box method (Coordinate Geometry) |

The triangle is equilateral | Area of an equilateral triangle |

- In the figure above, click on "hide details"
- Drag the vertices of the triangle to make a new shape
- Calculate the area using this method
- Click "show details" to verify your answer

- Triangle definition
- Hypotenuse
- Triangle interior angles
- Triangle exterior angles
- Triangle exterior angle theorem
- Pythagorean Theorem
- Proof of the Pythagorean Theorem
- Pythagorean triples
- Triangle circumcircle
- Triangle incircle
- Triangle medians
- Triangle altitudes
- Midsegment of a triangle
- Triangle inequality
- Side / angle relationship

- Perimeter of a triangle
- Area of a triangle
- Heron's formula
- Area of an equilateral triangle
- Area by the "side angle side" method
- Area of a triangle with fixed perimeter

- Right triangle
- Isosceles triangle
- Scalene triangle
- Equilateral triangle
- Equiangular triangle
- Obtuse triangle
- Acute triangle
- 3-4-5 triangle
- 30-60-90 triangle
- 45-45-90 triangle

- Incenter of a triangle
- Circumcenter of a triangle
- Centroid of a triangle
- Orthocenter of a triangle
- Euler line

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