Area of a Trapezoid Calculator
If you ever had problems with remembering the formulas in geometry class, this area of a trapezoid calculator is bound to help you. In just a few simple steps, you will be able to find the area of a trapezoid and determine all of its other properties, such as side lengths or internal angles. So, if you are troubled by questions like "how to find the perimeter of a trapezoid", look no further - simply keep reading to find out!
You can also check out our circumference calculator to analyze the geometry of a circle in more detail.
What is a trapezoid?
A trapezoid is a 4-sided geometrical shape with two sides parallel to each other. These two sides (a and b in the image above) are called the bases of the trapezoid. The other two sides (c and d) are called legs. h is the height of the trapezoid.
All internal angles of a trapezoid sum to give 360°. Additionally, the angles on the same side of a leg are called adjacent and always sum up to 180°:
α + β = 180°
γ + δ = 180°
How to find the area of a trapezoid?
Area of a trapezoid is found according to the following formula:
A = (a + b) * h / 2
You can notice that for a trapezoid with a = b (and hence c = d = h), the formula gets simplified to
A = a * h, which is exactly the formula for the area of a rectangle.
How to find the perimeter of a trapezoid?
You can also use the area of a trapezoid calculator to find the perimeter of this geometrical shape. Simply add all of the side lengths together:
P = a + b + c + d
Using the area of trapezoid calculator: an example
Let's assume that you want to calculate the area of a certain trapezoid. All the data given is:
α = 30°
γ = 125°
h = 6 cm
a = 4 cm
P = 25 cm
Calculate the remaining internal angles. As
α + β = 180°,
β = 180° - 30 ° = 150°.
γ + δ = 180°,
δ = 180° - 125° = 55°.
Find the lengths of the legs of the trapezoid, using the formula for the sine of an angle:
sin 30° = c / h
sin 55° = d / h
c = sin 30° * 6 = 12 cm
d = sin 55° * 6 = 7.325 cm
- Subtract the values of a, c, and d from the trapezoid perimeter to find the length of the second base:
b = P - a - c - d = 25 - 4 - 12 - 7.325 = 1.675 cm
- Finally, apply the formula for the area of a trapezoid:
A = (a + b) * h / 2 = (4 + 1.675) * 6 / 2 = 17.026 cm²
Make sure to take a quick look at the hexagon calculator, too!