How to Find the Area of a Triangle From Its Vertices

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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.

    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).

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

    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.

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

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

    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.

    Tips

    • To express absolute value, use two vertical lines, one on each side of the formula.

References

About the Author

Kelvin Hayes has been writing professionally since 2009 as a freelance copywriter. He runs his own online business, writing ebooks, reports and information products. Completely self-taught, Hayes prides himself on creatively completing writing projects by pulling from his wide range of life experiences.

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