How To Find The Area Of A Triangle From Its Vertices

To find the area of a triangle where you know the x and y coordinates of the three vertices, you'll need to use the coordinate geometry formula: area = the absolute value of Ax(By – Cy) + Bx(Cy – Ay) + Cx(Ay – By) divided by 2. Ax and Ay are the x and y coordinates for the vertex of A. The same applies for the x and y notations of the B and C vertices.

Step 1

Fill in the numbers for each corresponding letter combination within the formula. For example, if the coordinates of the triangle's vertices are A: (13,14), B: (16, 30) and C: (50, 10), where the first number is the x coordinate and the second is y, fill in your formula like this: 13(30-10) + 16(10-14) + 50(14-30).

Step 2

Subtract the numbers within the parentheses. In this example, subtracting 10 from 30 = 20, 14 from 10 = -4 and 30 from 14 = -16.

Step 3

Multiply that result by the number to the left of the parentheses. In this example, multiplying 13 by 20 = 260, 16 by -4 = -64 and 50 by -16 = -800.

Step 4

Add the three products together. In this example, 260 + (-64) + (-800) to get -604.

Step 5

Divide the sum of the three products by 2. In this example, -604 / 2 = -302.

Step 6

Remove the negative sign (-) from the number 302. The area of the triangle is 302, found from the three vertices. Because the formula calls for absolute value, you simply remove the negative sign.