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 of 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!
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 diagram) 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 do I find the area of a trapezoid?
To find the area of a trapezoid (
A), follow these steps:
- Find the length of each base (
- Find the trapezoid's height (
- Substitute these values into the trapezoid area 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 do I find the perimeter of a trapezoid?
To quickly find the perimeter of a trapezoid, follow these steps:
- Find the length of all sides of the trapezoid (
- Add them together to get the perimeter of the trapezoid:
P = a + b + c + d.
- That's it! It is that simple.
Or you can alternatively use the area of a trapezoid calculator, which will automatically find the area and perimeter of the trapezoid for you.
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!
How is a trapezoid different from other quadrilaterals?
Trapezoids differentiate themselves from other quadrilaterals because they have exactly one pair of parallel sides. They are, in fact, quadrilaterals, like rectangles and squares, but they are not parallelograms.
What is the area of a trapezoid with height 5 meter and bases 8 meter and 1 meter?
The area of this trapezoid is 22.5 meters squared. To get the result, we use the area of a trapezoid formula:
A = (a + b) × h / 2 and place
a = 8 m,
b = 1 m, and
h = 5 m inside it.