Posted by **Millwe** on Thursday, November 3, 2011 at 9:04pm.

On a graph, the points (4,-2),(7,-2),(9,-5) and (2,-5) are connected in order to form a trapezoid. To the nearest tenth, what is its perimeter?

- geometry -
**drwls**, Thursday, November 3, 2011 at 10:44pm
Compute the four side lenghts using the pairs of coordinates.

The side that goes from (4,-2) to (7,-2) has a length of sqrt[(7-4)^2 + (2 -(-2)^2] = 5

Do the others the same way.

Then add all four.

- geometry -
**Millwe**, Thursday, November 3, 2011 at 11:09pm
Thank you for your help, I still don't understand

- geometry -
**Steve**, Friday, November 4, 2011 at 12:10pm
In order to figure the length of a line segment, you have to rely on the Pythagorean Theorem. If that doesn't sound familiar, you need to review your text. The theorem states that in a right triangle with legs a and b, with hypotenuse c,

c^{2} = a^{2} + b^{2}

Now, if you plot two points on a piece of graph paper, such as (7,-2) and (9,-5), the line joining the points will be a slanting line. If you draw horizontal and vertical lines from each point, they will intersect to form a right triangle. The length of the legs are just the x-distance from 7 to 9 = 2, and the y-distance from -5 to -2 = 3.

So, the length of the hypotenuse is given by

h^{2} = 2^{2} + 3^{2}

h^{2} = 13

so,

h = √13

If you follow these steps for each side of the figure, you can add up all the lengths to get the perimeter.

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