Welcome to the trapezoid calculator, a tool with which you'll be able to:
- Calculate the trapezium area;
- Find the trapezoid height;
- Calculate the trapezoid perimeter; and
- Calculate the trapezoid angles.
Read on if you want to learn how to find the trapezoid height, area, or perimeter using the formulas.
Trapezoid perimeter and angles
The perimeter of a polygon, be it regular or irregular, is the sum of its side lengths, and trapezoids are not the exception. Therefore, the perimeter of a trapezoid is the sum of its four sides:
P = a + b + c + d
Like any other quadrangle, the sum of angles in a trapezoid is 360 degrees (or 2π radians). However, being a trapezoid (i.e., having a pair of parallel sides) forces an additional property, which says that the pair of angles along one of the legs are supplementary angles. Therefore, their sum must equal 180 degrees (or π radians), which in notation from the calculator figure, translates into:
α + 𝛾 = β + δ = 180°
How to calculate trapezoid area
A trapezium is like a rectangle that has "fallen over" slightly. Therefore, we calculate its area in a similar way to the area of a rectangle.
To calculate a trapezoid area, use the following formula:
A = h × (a + b)/2
- A — Trapezium area;
- h — Trapezoid height; and
- a and b — Trapezoid bases.
You can look at the dimensions in the following image:
For example, to calculate the area of a trapezoid whose bases are a = 6 in and b = 5 in with height h = 4 in:
A = 4 in × (6 in + 5 in)/2
A = 4 in × (11 in)/2
A = 4 in × 5.5 in
A = 22 in2
If the formula seems confusing to you, you can follow these steps to obtain the result:
- Sum the bases of the trapezoid. In this case: a + b = 6 in + 5 in = 11 in
- Divide the previous result by two. In this case: (11 in)/2 = 5.5 in
- Multiply the previous result by the height. In this case: 4 in × 5.5 in = 22 in
But what if you don't know h? Let's see how to find the trapezoid height.
How to find the height of a trapezoid
The equation to find the height relies on trigonometric functions. The formula is:
h = c × sin(α) = d × sin(δ)
As you can see, to calculate the height, you need to know:
- The side c and the angle α; or
- The side d and the angle δ.
An acute trapezoid
An obtuse trapezoid
For example, to calculate the height of a triangle with c = 5 in and α = 22 degrees:
h = 5 in × sin(22°)
h = = 5 in × 0.3746
h = = 1.873 in
You can learn more about trigonometric functions with our trigonometric functions calculator.