Area Calculator using Perimeter for Triangles

Enter the perimeter of an equilateral triangle:

Here is a table summarizing how to calculate the area of a triangle using the perimeter:

Triangle Type	Given Information	Formula for Area	Remarks
Equilateral Triangle	Perimeter is given	Square root of three divided by four times the square of one side, where the side is found by dividing the perimeter by three	Since all sides are equal, the side length is perimeter divided by three
Scalene Triangle	Perimeter and all three sides are given	Square root of the product of semi-perimeter, semi-perimeter minus first side, semi-perimeter minus second side, and semi-perimeter minus third side	Uses Heron's formula, where semi-perimeter is found by dividing the perimeter by two
Right Triangle	Perimeter, hypotenuse, and one side are given	One-half times the product of the two shorter sides	If only perimeter is known, first solve for side lengths using perimeter equation
Isosceles Triangle	Perimeter and base are given	One-half times base times height, where height is found using the Pythagorean theorem	Two sides are equal, so use perimeter to find the side lengths