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!

You can also check out our circumference calculator to analyze the geometry of a circle in more detail or our circle formula calculator to learn more about the equations behind that geometry.

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°

To find the area of a trapezoid (A), follow these steps:

1. Find the length of each base (a and b).
2. Find the trapezoid's height (h).
3. 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.

To quickly find the perimeter of a trapezoid, follow these steps:

1. Find the length of all sides of the trapezoid (a, b, c, and d).
2. Add them together to get the perimeter of the trapezoid: P = a + b + c + d.
3. 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.

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

1. Calculate the remaining internal angles. As α + β = 180°, β = 180° - 30 ° = 150°.

2. Similarly, as γ + δ = 180°, δ = 180° - 125° = 55°.

3. Find the lengths of the legs of the trapezoid, using the formula for the sine of an angle:

   sin 30° = h / c

   sin 55° = h / d

   c = 6 / sin 30° = 12 cm

   d = 6 / sin 55° = 7.325 cm

4. 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

5. 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!