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### Course: High school geometry>Unit 6

Lesson 3: Problem solving with distance on the coordinate plane

# Area of trapezoid on the coordinate plane

Sal finds the area of a trapezoid using the distance formula and the trapezoid area formula.

## Want to join the conversation?

• I do not know how to do all the shapes that you give on the the exercise
• Why are you using things like "6 square roots of 5" when you could just put the square root of 180 in a calculator and be done with it? It seems to me like you're just adding a bunch of steps and making it far more complicated than it needs to be.
• The one issue is the difference between an exact answer and an rounded answer, 6 √5 is the exact answer simplified, using a calculator will require you to round.
• My geometry teacher says that in order for the height to be a height in a trapezoid it needs to be perpendicular to one of the bases. Is this true for ALL trapezoids? And sorry I ask a lot of questions.
• Height is always perpendicular to the base, that is true for all figures, triangles, rectangles, parallelograms, and trapezoids
• I worked through a perimeter problem which at the end had me with 8 + √89 + √89 + √32. I added all the square roots together and got:

8 + √89 + 89 + 32
= 8 + √210
They wanted a decimal to the tenth so I finished with ≈22.5.
However, that was wrong instead they did took the square roots before adding:

8 + √89 + √89 + √32
≈ 8 + 9.43 + 9.43 + 5.66
And got ≈32.5.

So obviously these come out with two vastly different answers. So what are the rules here why is this approach the correct one?
Thanks!
• You can't add the contents of square roots. If you could, then √(9)+√(16) would equal √(9+16)
√(9)+√(16) = 3+4 = 7
√(9+16) = √(25) = 5

Hopefully you can see that adding the contents of radicals doesn't work. This is why they did the square roots first. Since each of the square roots creates an irrational number, the results were rounded.

Hope this helps.
• I'm in sixth grade math and I don't know how to do what you did at .
• That was just another way of doing the Pythagorean Theorem to find the longest side of a right triangle.
a^2 + b^2 = c^2, where "c" is the longest side of the triangle.
Since you have to find the square root anyway, you can put the "a^2 + b^2" in a square root and immediately solve for "c".
So all Sal did here was do two steps at once.
• So you guys don't have any explanation on perimeters. Can you explane how to find the Perimeter of a Trapizoid on a coordinate plane?
• once you've found the lengths of all the sides using the Pythagoras theorem, instead of plugging those values into the area formula, simply add them up.
• Any videos on Khan Academy that explains how to calculate for example √9*5 into ∛5? Or maybe someone can explain the logic. It seems that the 3 before the √ came from the fact that it is the square root of 9. Yet I don't get equivalent answers from the following equations, which would be applying my logic: √4*8 and 2√8, so I must be missing something.
• So the first issue is that you show the cubed root rather than 3√5 which is different. The logic is that √(9*5) can be separated to √9*√5, and since √9 = 3, you get 3√5. The second issue is that your problem is not completely simplified. So √(4*8) (notice I keep adding parentheses) can be shown as √(4*4*2) = √4*√4*√2 = 2*2*√2=4√2. I am not sure what you mean by not getting equivalent answers except for the fact that you did not break 8 down into a perfect square * a non-perfect square.
• Ok that makes sense but i still dont understand how to find the piermeter on a coordinate plane with points, idk why but something is just not clicking in my brain