In the future, I hope to add Physics and Linear Algebra content. Topics cover Elementary Math, Middle School, Algebra, Geometry, Algebra 2/Pre-calculus/Trig, Calculus and Probability/Statistics. If you have any requests for additional content, please contact Andy at He will promptly add the content. Where A is the area, a is the length of the side.\(\,\,\,\,\,\,\text\)Ī is a free math website with the mission of helping students, teachers and tutors find helpful notes, useful sample problems with answers including step by step solutions, and other related materials to supplement classroom learning. This is just simplified Heron's formula because all sides are equal. Well, you can also compute the cartesian distance between the vertexes and use Heron's formula. Where A is the area, and x and y are coordinates of triangle vertexes. If the vertexes have coordinates like (x1, y1), (x2, y2) and (x3, 圓) then the formula is Using this formula, you can find a triangle area if you know the cartesian coordinates of all three vertexes of a triangle. Where A is the area, a and b are the sides' lengths, alpha is the angle at the common vertex.Īctually, this form directly follows from half of the base times height formula because the triangle's height would be. Side-angle-side formulaĪlso referred to as SAS, this formula allows you to find a triangle area if you know two sides and the angle at a common vertex (included angle). A proof can be found in his book Metrica written around 60 AD. The formula is named after Hero of Alexandria, a Greek Engineer and Mathematician, in 10 - 70 AD. Where A is the area, a, b, c are the lengths of the sides, p is the perimeter divided by 2 (semi-perimeter). You can find the area of a triangle if you know the lengths of all sides. Where A is the area, a is the length of the base, h is the altitude's length. Any side can be the base, but the altitude must correspond to the base. You can find the triangle area from the length of the base and the length of the corresponding altitude. You can find all formulas below the calculator. This formula is derived from Heron's formula and uses only the length of one side to calculate the area. This formula uses the coordinates of the vertices to find the length of the sides of the triangle and then uses Heron's formula to find the area.įinally, if you are dealing with an equilateral triangle, there is a simplified formula that can be used. If you know the coordinates of the three vertices of the triangle, you can use the Coordinates formula. This formula uses the two side lengths and the included angle to calculate the area of the triangle. If you know two sides and the included angle of the triangle, you can use the Side-angle-side formula to find the area. Heron's formula is useful when you do not know the height of the triangle or when the triangle is not a right triangle. This formula uses the three side lengths to calculate the semiperimeter, which is then used to find the area of the triangle. If you know all three sides of the triangle, you can use Heron's formula. This formula takes half of the base length and multiplies it by the altitude length to find the area. If you know the base and the altitude of the triangle, you can use the Half of base times height formula.
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