Triangle Area from Coordinates
This calculator helps you find the area of a triangle when you know the coordinates of its three vertices. Just enter the (x, y) coordinates for each point, and we'll do the math using the Shoelace Formula.
e.g., 1
e.g., 1
e.g., 4
e.g., 2
e.g., 2
e.g., 5
This calculator helps you find the area of a triangle when you know the coordinates of its three vertices. Just enter the (x, y) coordinates for each point, and we'll do the math using the Shoelace Formula.
Area = 0.5 * |(x₁y₂ + x₂y₃ + x₃y₁) - (y₁x₂ + y₂x₃ + y₃x₁)|
Let's say your triangle has vertices at A(1,1), B(4,2), and C(2,5). Using the Shoelace Formula: Step 1: Write down the coordinates in a column, repeating the first point at the end: (1, 1) (4, 2) (2, 5) (1, 1) Step 2: Multiply diagonally downwards and sum these products: (1 * 2) + (4 * 5) + (2 * 1) = 2 + 20 + 2 = 24 Step 3: Multiply diagonally upwards and sum these products: (1 * 4) + (2 * 2) + (5 * 1) = 4 + 4 + 5 = 13 Step 4: Subtract the second sum from the first sum: 24 - 13 = 11 Step 5: Take the absolute value and multiply by 0.5: Area = 0.5 * |11| = 5.5 square units. Our calculator will quickly give you this result!
The Shoelace Formula (also known as the surveyor's formula or Gauss's area formula) is a method to determine the area of a polygon whose vertices are described by Cartesian coordinates. For a triangle, it involves summing the cross-products of the coordinates and taking half the absolute value of the result.
If the calculated area is zero, it means the three points you entered are collinear. In other words, they all lie on the same straight line and do not form a triangle with a measurable area.
For the Shoelace Formula, the absolute value ensures you get a positive area regardless of the order you list the vertices (clockwise or counter-clockwise). However, if you were calculating signed area, the order would matter.
Yes, this formula works for any triangle, whether it's acute, obtuse, right-angled, equilateral, isosceles, or scalene. As long as you have the coordinates of its three vertices, you can find its area.
Triangle Area from Coordinates: The Shoelace Formula Explained
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