Formulas for Trapezoids

Define Trapezoid

Definition of a Trapezoid

A trapezoid is a quadrilateral with one pair of parallel sides. Some people would say "exactly" one pair, while others would say "at least" one pair. Generally, a trapezoid has "at least" one pair of parallel sides.

Is a trapezoid a parallelogram?

A trapezoid is not a parallelogram.

But a parallelogram is a trapezoid. (using the "at least" definition. With the "exactly" definition, a parallelogram is not a trapezoid either)

Properties of trapezoids quick reference

Property
Information
Sides
4
Parralel sides
At least one pair
Sum of interior angles
360 degrees
Isosceles
If the non-parallel sides are equal
Base
One of the parallel sides
Height/Altitude
The length of the line perpendicular to both bases
Area Formula
height * (base1 + base2)/2
Area Formula 2
height * median
Median
line segment halfway between the bases

Isosceles trapezoids

Isosceles trapezoids are trapezoids where the two nonparallel sides are equal. Isosceles triangles are the most used real life.

Midsegment of a trapezoid

The midsegment of a trapezoid, also known as the median of a trapezoid, is the line halfway between the bases. Because of this "halfway" status, it also happens to have a length half of the sum of the bases.

The median is always parallel to the bases.

Finding the height of a trapezoid

The height, or altitude, of a trapezoid is the perpendicular line between both bases.

Normally you have to measure it out but there are some formulas you can use if you have the necessary information

  • Height = Area / Median
  • You can also use the pythagorean algorithm if you were given a triangle that makes up the sides
  • Likewise, if you have one of the side (hypotenuse) and an angle, you can use trigonometry.

Perimeter of a trapezoid

There is no neat formula for the perimeter of a trapezoid other than

  • perimeter = side + side2 + base1 + base 2.
  • In other words, just add up all the sides.

For an iscosceles trapezoid, the perimeter formula can be shortened to

  • perimeter = 2 * side + base 1 + base 2.

Finding the perimeter of a trapezoid when you have the median

If you don't have the bases, but you have the median, new perimeter of a trapezoid formulas occur:

  • perimeter = side1 + side2 + 2 * median
  • (for isosceles) perimeter = 2 * (side + median)

Area of trapezoids

The area of a trapezoid is the height times the average of the bases. The formula doesn't change for the area of isosceles trapezoid.

  • Area = height * (base 1 + base 2) /2

It can also be said that the area of trapezoids can be acquired by doing the height times the length of the median, since the median will always equal the average of the bases.

  • Area = height * median

Finding the area of a trapezoid without a formula

If, for whatever reason, you do not have a formula, just remember that a trapezoid is merely the composition of a square and two triangles. You can use the square and triangle area formulas in order to find the area of area of trapezoids if necessary.


Trapezoid angles

The sum of the interior angles of a trapezoid is 360 degrees, like all quadrilaterals.

Isosceles trapezoid angles

If your trapezoid is isosceles, there are other things you will know about your trapezoid. Both interior angles next to a base are congruent!

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Comments 3 comments

Docmo profile image

Docmo 5 years ago from UK

Really useful for helping with homework! Great, thanks.


Mio 23 months ago

1. What is the difference beeetwn a parallelogram and a trapezoid?Well that's obvious they are spelled completely different.2. True or False. All squares are rectangles.True.3. True or False. All rectangles are squares.False, some of them are actually cool, the rest though are squares.4. Can a triangle have more than one obtuse angle?No. Unless it is talking to Steve, in which case it would probably end up very, very obtuse.5. What is a dodecagon?He was one of the transformers, I think the little one that could turn into a radio.


Ian 23 months ago

I liked this video a lot when I first saw it. Yes, it's not a rigorous proof that I had to learn in sohcol. But I think it's a great starting point for a conversation. And it's a lot less scary. So, as an intro or a supplement to the topic it works. Plus I can see how it can open up a conversation about how close should a "close enough" be, precision, and approximation error. Yelena recently posted..Last-Minute Christmas Decorations and Tangled Lights Reply

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