Have you ever needed to know the area of a trapezoid? What about finding the perimeter of a trapezoid? If you’ve forgotten the formula or need help, try this area of a trapezoid calculator.

This tool can work out the area of a trapezoid, side lengths, and internal angles. Read on to find out more.

The Definition of a Trapezoid

If you want to know what a trapezoid is, then you’ve come to the right place. A trapezoid is four-sided with two parallel sides. Those two sides (a and b) are the base of the trapezoid. The other two sides (c and d) which are not parallel are the legs. You also have the height, which is h. 

When you measure all the internal angles of a trapezoid, they equal 360 degrees. The angles along the side of the leg are adjacent and equal 180 degrees. The formulas for these measurements look like this: 

α + β = 180°

and 

γ + δ = 180°

How Does One Find the Area of a Trapezoid?

Finding the area of a trapezoid is straightforward with one simple formula: 

A = (a + b) x h / 2

When a = b (with both lengths the same), then c = d = h. Next, simplify the formula to A = a x h. Does that formula look familiar? It’s the same one you use for the area of a rectangle.

How Does One Find the Perimeter of a Trapezoid?

If you thought finding a trapezoid’s area was easy, then the perimeter will surprise you. Add all the length measurements of the sides together. 

P = a + b + c + d

An Example of How to Use the Area of a Trapezoid Calculator

Sometimes, it’s helpful to have a real-life example to understand the calculator’s inner workings. In this example, we have all the data we need. 

α - 30°
γ - 125°
h – 6 cm  
a = 4 cm
P = 25 cm

Now you just follow these steps.

1.	Calculate the internal angles 
α + β = 180°

β = 180° - 30 ° = 150°

γ + δ = 180°

δ = 180° - 125° = 55°

2.	Find the leg length measurements of the trapezoid. Use the sine of an angle formula. 
sin 30° = c / h

sin 55° = d / h

c = sin 30° x 6 = 12 cm

d = sin 55° x 6 = 7.325 cm

3.	Take the values of a, c, and d, away from the perimeter of the trapezoid. You get the second base length. 

b = P - a - c - d = 25 - 4 - 12 - 7.325 = 1.675 cm

4.	Apply the trapezoid area formula 
A = (a + b) x h / 2 = (4 + 1.675) x 6 / 2 = 17.026 cm²