Trapezoid Area Calculator

A trapezoid is a quadrilateral with at least one pair of parallel sides. The two parallel sides are called the bases and the perpendicular distance between them is called the altitude or height. This calculator will determine the missing value given three values for any combination of base, height and area.

It doesn't just calculate the area. Once the shape is determined, other values such as midlines are also shown. In addition, perimeter, legs, both base angles, diagonals and a simplified material cost calculation can be determined.

Formula for area of a trapezoid:

Add both bases, find their average, and multiply that by the height.

where a and b are the two parallel bases and h is the perpendicular height. For example, a trapezoid with one base of 8 meters, another base of 1 meter, and a height of 5 meters.

The order of the two bases does not matter. The average, calculated by adding and dividing by 2, will remain the same regardless of the order. So you can call the shorter side a and the longer side b or vice versa.

Why are we taking the average of the two bases?

The area of a rectangle is the product of its length and width. In a trapezoid, the widths change across the shape so there's no single width to use. So we'll use the average of the two bases as a substitute for the width.

This average is exactly the same as the midline. The midline is a line that goes through the middle of the height of the figure and is parallel to both bases. So the area is the product of the midline and the height, and the area of the trapezoid is equal to the area of a rectangle with a width equal to the length of the midline.

Here's how to use this calculator:

Enter the short base, long base and height then check out the result in the output field. For each field you can set a separate unit so for example you can enter one base in centimeters and another in inches. The calculator will first convert all values to the same unit before performing the calculation.

The height is the vertical distance between the two bases and must be measured along a line perpendicular to both bases. It is not the hypotenuse. Using the length of the sides instead of the height is a common error that will always result in an overestimate of the area.

conversion

Since the four measurements are linked by a single equation, any three of them can be used to calculate the remaining value. If you leave the area blank, it will be calculated for you, and if you enter the area, the other values will be converted.

If you enter the area and two base sides and leave the height free, then the height is calculated. If you enter the area, the height and one base side and leave the other base side free, then this base side is calculated. If the entered numbers do not represent a real trapezoid, e.g. if the given area for the given height and base sides is too small, then the calculation tool does not return a negative value but indicates this as an issue.

Midline, circumference, thighs

The median line is the average of the two bases and does not require any other data. The perimeter requires all four sides, so the two bases and the two legs are added together.

With just the two bases and the height, it is not possible to determine the legs uniquely since the area does not change if you move the top side left or right. If it is known that the trapezoid is an isosceles trapezoid (i.e., both legs are of equal length), then the legs, diagonals and base angles can be calculated from the two bases and the height. You can check these values by activating the plane for isosceles trapezoids. Alternatively, you can activate the perimeter plane and enter the measured values for the two legs.

Trapezoid types

An isosceles trapezoid has two sides of equal length, which leads to symmetry and the base angles being congruent in pairs. A right trapezoid has two right angles, making one of the legs perpendicular and also the height. An irregular trapezoid has all four sides different lengths and no particular symmetry.

The inclusive definition used here means that every parallelogram is a trapezoid. This is because a parallelogram has two pairs of parallel sides. If the two bases are equal in length, then the formula for area becomes the product of base and height, which is the rule for finding the area of parallelograms and rectangles.

Divide a Trapezoid Into Two Triangles

A diagonal divides a trapezoid into two triangles. One triangle is on the shorter side and one is on the longer side. Both have the same height as the whole trapezoid.

The area of one triangle is a multiplied by h and divided by 2, while the area of the other triangle is b multiplied by h and divided by 2. When you add both areas together, you get back to the formula for the area of a trapezoid. A pie chart showing the area breakdown illustrates this breakdown based on the values entered.

Examples of calculations:

The table shows the areas of some trapezoids, with results rounded to two decimal places. The last row uses a traditional example where a trapezoid with bases of 5 and 7 centimeters and a height of 6 has an area of 36 square centimeters.

Applications of area calculation for trapezoids:

It is most commonly used in land or roof construction work. Fields or plots of ground typically have two parallel sides of different lengths, giving the shape a trapezoidal form. The survey documents will contain these two sides as well as the horizontal distance between them.

Cross-sections of canals, dams, levees and drainage ditches are usually trapezoidal. Therefore estimates for dredging and earthwork operations are based on this formula. When a designer needs to calculate the amount of material for tapering parts, this shape is also used in table tops, lampshades and handbag panels.

Tips for accurate results:

Please measure the two base sides and height in the same unit of measurement if possible. If you use different units manually it will usually result in an incorrect answer. The calculator can convert but make sure to enter the correct unit for each field.

Always measure vertically from one base to the other. If you only know the hypotenuse and an angle, first calculate the vertical height and then input it.