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Area of a Trapezoid Calculator

Given an arbitrary trapezoid, this calculator will figure out the area.

The formula for area of a trapezoid can be difficult to derive or memorize for some, but it's really just a variation of the area of a triangle.  But if memorizing formulas is a hindrance, you can use this calculator which will determine everything you need to know about the area and perimeter of a trapezoid.

For beginners in geometry, you may be confused as to what is a trapezoid.

A trapezoid is a quadrilateral (4- sides since quad means 4) in which two of the sides are parallel to each other.  We can label those sides a and b with the remaining sides as c and d. We will use these variable designations in the formula for perimeter and area later.

One property of a trapezoid and all quadrilaterals is that the sum of the interior angles is 360 degrees and the sum of the same side interior angles always add up to 180 degrees.

What is the area of a trapezoid?

The formula is given by

A = (1/2)(a + b)h, where h is the height of the trapezoid.

Notice how this is very similar to the area of a triangle, which is A = (1/2)bh.

To calculate the perimeter of the trapezoid, simply add the lengths of all the sides, therefore 

P = a + b + c + d

Here's an example that can be computed manually.

Suppose we know sides a and b and height h

a = 4 cm

b = 6 cm

h = 3 cm

Inputting these values into the formula you get

A = (1/2)(4 + 6)(3)

A = (1/2)(10)(3)

A = (1/2)(30)

A = 15 square cm

Note that our calculator can find the area using length in units from millimeters to kilometers and from inches to miles.

If you know the other two sides, c and d, then calculating the perimeter of a trapezoid is simple. Suppose in addition to a = 4 cm, b = 6 cm, we know that c = 5 cm and d = 2 cm. Therefore the perimeter of the trapezoid is 4 + 6 + 5 + 2 = 17 cm.

Check out our other geometry calculators for areas of other geometric figures.

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