What Is a Trapezoid Calculator?
A trapezoid (called a trapezium in British English) is a four-sided polygon with exactly one pair of parallel sides. These parallel sides are the two bases, labeled a and b, and the perpendicular distance between them is the height (h). This calculator finds the area of any trapezoid in one step from those three measurements, and also reports the median (mid-segment) length.
How to Use It
Enter the length of the top base a, the bottom base b, and the height h. All three should be in the same unit (cm, m, inches, etc.). Press calculate and the tool returns the area in those squared units. The order of the two bases does not matter because they are simply averaged.
The Formula Explained
The area of a trapezoid is the average of its two parallel sides multiplied by the height:
$$\text{Area} = \frac{a + b}{2} \times h$$
Intuitively, averaging the two bases produces the length of the median line that sits halfway up the shape. Multiplying that average length by the height behaves just like the area of a rectangle, which is why the formula works for any trapezoid regardless of how slanted the sides are.
Worked Example
Suppose a trapezoid has a top base of 8, a bottom base of 12, and a height of 5. First average the bases: \((8 + 12) / 2 = 10\). This is the median. Then multiply by the height: \(10 \times 5 =\) 50 square units.
FAQ
Does it matter which base I call a or b? No. Because the formula averages them, swapping a and b gives the same area.
What is the height? The height is the perpendicular (straight-up) distance between the two parallel bases — not the length of a slanted side.
What is the median? The median, or mid-segment, is the segment joining the midpoints of the two non-parallel sides. Its length equals \((a + b) / 2\).
