![]() ![]() 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. cosγ using the notation from our calculator graph.Īnother rule, supported by our perimeter of a triangle calculator is for right-angled triangles only: in such a triangle, if you are given the length of the hypotenuse and one of the other sides, you can easily compute the perimeter using the Pythagorean theorem.If you know the base and the altitude of the triangle, you can use the Half of base times height formula.The law of sines basically states that each side and its opposing angle's sine are related in the same way: The law of cosines is a generalization of the Pythagorean theorem and states that c 2 = a 2 + b 2 - 2ab Many of the above rules rely on the Law of Sines and the Law of Cosines, so if you are not familiar with them, it might be a bit tricky to understand them. ASA (angle-side-angle) - having the measurements of two angles and the side which serves as an arm for both (is between them), you can again solve the triangle fully.SSA (side-side-angle) - having the lengths of two sides and a non-included angle (an angle that is not between the two), you can solve the triangle as well.SAS (side-angle-side) - having the lengths of two sides and the included angle (the angle between the two), you can calculate the remaining angles and sides, then use the SSS rule.Just sum them up according to the formula above, and you are done. SSS (side-side-side) - this is the simplest one in which you basically have all three sides. ![]() So, how to calculate the perimeter of a triangle using more advanced rules? As mentioned above, there are several different sets of measurements you can start with, from which you can solve the whole triangle, meaning you can arrive at the length of its sides as well. These ways have names and abbreviations assigned based on what elements of the triangle they include: SSS, SAS, SSA, AAS and are all supported by our perimeter of a triangle calculator. However, given different sets of other values about a triangle, it is possible to calculate the perimeter in other ways. The formula for the perimeter of a triangle T is T = side a + side b + side c, as seen in the figure below: Examples: find the perimeter of a triangle. ![]()
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