Trapezoid Area Calculator

Area is a numerical characteristic of a two-dimensional (flat or curved) geometric figure, informally speaking, showing the size of this figure. Historically, the calculation of the area was called quadrature. A figure having an area is called quadratic. Find the area of more than 22 shapes (triangle, square, pentagon, etc.) using our amazing calculator.

Quadrangle — in which two sides are parallel and the other two sides are not parallel is called a trapezoid. Parties that are not parallel are called the sides of the trapezoid.

Calculating the area of a trapezoid can be challenging, especially if you don't have a lot of experience with geometry. That's why we've created this trapezoid area calculator – to make it easy for you to find the area of a trapezoid no matter what information you have.

Formulas for Trapezoid Area

Here are the formulas for calculating the area of a trapezoid based on different information:

Area of Trapezoid by Diagonals and Angle

If you know the lengths of the two diagonals and the angle between them, you can use the following formula to find the area of a trapezoid:

S = \dfrac{1}{2}d_1*d_2*sin(\alpha)

The area of a trapezoid across the diagonals and the angle between them is considered the conditional division of the trapezoid into four triangles, just like the area of any arbitrary quadrangle.

Area of Trapezoid by Midline and Height

If you know the length of the midline (the average of the two bases) and the height of the trapezoid, you can use the following formula to find the area:

S = m*h

The proof of this formula will be the representation of the area of the trapezoid as the sum of the areas of two triangles obtained during the diagonal.

Area of Trapezoid by Lateral Sides and Bases

If you know the length of the two lateral sides and the length of the two bases, you can use the following formula to find the area of a trapezoid:

S = \dfrac{a+b}{2}\sqrt{c^2 - \left( \dfrac{(b-a)^2 + c^2 -d^2}{2(b-a)} \right)^2}

By drawing two heights in the trapezoid, we get right triangles with known hypotenuse and unknown legs. Through the Pythagorean theorem, we express height in right triangles, after with substitutions we obtain the above-mentioned formula.

Area of Trapezoid by Side and Base

If you know the length of one of the sides of the trapezoid and the length of one of the bases, you can use the following formula to find the area:

S = \dfrac{1}{2}(a+b)h

This formula is based on the fact that the area of a trapezoid can be calculated as half the product of one of the bases multiplied by the height and the sine of the angle between them.

Area of Trapezoid by Inscribed Circle Radius

If you know the radius of the circle inscribed in the trapezoid and the length of one of the bases, you can use the following formula to find the area:

S = r * (a + b)

The area of an isosceles trapezoid can be found in another way, if known angle at the base and the radius of the inscribed circle. The fact is that the center of the inscribed circle, from where the radius originates, is located exactly in the center of the trapezoid, thus equalizing the height and diameter of the circle (or doubled radius) we can find the middle line, from here we get the trapezoid area formula:

S = \dfrac{4r^2}{sin(\alpha)}

Using the Trapezoid Area Calculator

Our trapezoid area calculator makes it easy to find the area of your trapezoid. Simply select the method that corresponds to the information you have available and enter the values in the appropriate boxes. The calculator will automatically calculate the area for you.

Conclusion

Calculating the area of a trapezoid can be a daunting task, but with the formulas and calculator we've provided, it doesn't have to be. Try it out for yourself and see how easy it can be to find the area of a trapezoid, no matter what information you have available.