Calculate trapezium or trapezoid area from two bases and height or midline and height. Reverse solve a missing base, height or midline.
This calculator finds the area of a trapezium from two bases and height or from midline and height. It also works in reverse when the area is known and you want to solve for a missing base, the height, or the trapezium midline.
area of a trapezium
two bases and height
midline and height
The standard trapezium area formula is A = ((a + b) / 2) × h. Because the average of the two parallel bases is the midline m, the same formula can also be written more simply as A = m × h.
A = ((a + b) / 2) × h
midline m
A = m × h
That makes the midline a useful extra result as well: when two bases are known, the calculator can also show m = (a + b) / 2. In American English, this same shape is usually called a trapezoid.
m = (a + b) / 2
trapezoid
$$A= \frac{a+b}{2} \times h$$
How do you calculate the area of a trapezium?Use A = ((a + b) / 2) × h, where a and b are the two parallel bases and h is the height.
a
b
h
What is the trapezium area formula using the midline?If m is the trapezium midline, then A = m × h. The midline is the average of the two bases: m = (a + b) / 2.
m
Can I find a missing base from the area and height?Yes. Rearranging the formula gives a = (2A / h) - b or b = (2A / h) - a, depending on which base is missing.
a = (2A / h) - b
b = (2A / h) - a
Can I find the trapezium height from the area and two bases?Yes. Solve the area formula for height: h = 2A / (a + b).
h = 2A / (a + b)
What is the difference between a trapezoid and a trapezium?The naming depends on regional convention. On this site the primary term is trapezium, while in American English the same shape is usually called a trapezoid.
trapezium
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