How to Find the Perimeter Using the Distance Formula

The distance formula stems from the Pythagorean Theorem and is used to calculate separation between any two points that are given in Cartesian coordinates. Distance equals to sqrt((X2 - X1)^2 + (Y2 - Y1)^2); X1,Y1 and X2,Y2 are Cartesian coordinates of the two points and "sqrt" is an abbreviation for the root square math operation. Perimeter of a geometrical shape is the sum of the lengths of all its sides. As an example, calculate the perimeter of the triangle defined by three points with following X and Y coordinates: (1.4, 2.0), (3.4, 6) and (-1,-1.8).

Things You'll Need

• Calculator

Instructions

1. Subtract the coordinate "X" of the first point from the coordinate "X" of the second point, and raise the difference to the power of 2.
   In our example, it will be: (3.4 -- 1.4)^2 = 4.

2. Subtract the coordinate "Y" of the first point from the coordinate "X" of the second point, and raise the difference to the power of 2.
   In our example, it will be: (6 -- 2)^2 = 16.

3. Add up values from Step 1 and 2, and then take the square root of the sum to calculate the length of the side defined by the first and second points. In this example, this length = sqrt(16 + 4) = sqrt(20) = 4.47. Note that the result is rounded to hundredths.

4. Subtract the coordinate "X" of the second point from the coordinate "X" of the third point, and raise the difference to the power of 2.
   In our example, it will be: (-1 - 3.4)^2 = 19.36.

5. Subtract the coordinate "Y" of the second point from the coordinate "Y" of the third point, and raise the difference to the power of 2.
   In our example, it will be: (-1.8 - 6)^2 = 60.84.

6. Add up values from Step 4 and 5, and then take the square root of the sum to calculate the length of the side defined by the second and third points. In this example, this length = sqrt(19.36 + 60.84) = sqrt (80.2) = 8.96 (rounded to hundredths).

7. Subtract the coordinate "X" of the third point from the coordinate "X" of the first point, and raise the difference to the power of 2.
   In our example, it will be: (1.4 -- (-1))^2 = 5.76.

8. Subtract the coordinate "Y" of the third point from the coordinate "Y" of the first point, and raise the difference to the power of 2.
   In our example, it will be: (2 -- (-1.8))^2 = 14.44.

9. Add up values from Step 7 and 8, and then take the square root of the sum to calculate the length of the side defined by the first and third points. In this example, this length = sqrt(5.76+ 14,44) = sqrt (20.2) = 4.49 (rounded to hundredths).

10. Add up the side lengths from Steps 3, 6 and 9 to calculate the perimeter. In the example, Perimeter = 4.47 + 8.96 + 4.49 = 17.92.

References

• "The Distance Formula," Elizabeth Stapel, Purplemath.com.