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Formulas for Trapezoids
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
At least one pair
Sum of interior angles
If the non-parallel sides are equal
One of the parallel sides
The length of the line perpendicular to both bases
height * (base1 + base2)/2
Area Formula 2
height * median
line segment halfway between the bases
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.
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!