Introduction
A trapezoid is a four-sided shape with exactly one pair of parallel sides. These parallel sides are called the bases, and the distance between them is called the height. To find the area of a trapezoid, you add the two bases together, multiply by the height, and then divide by 2. The formula looks like this: Area = (base 1 + base 2) × height ÷ 2. This Trapezoid Area Calculator finds the area from the measurements you enter. Just enter the lengths of the two bases and the height, and it will give you the area right away. It works for any trapezoid, no matter how long or short the sides are, as long as you know the two bases and the height.
How to Use Our Trapezoid Area Calculator
Enter the lengths of the two parallel sides and the height of your trapezoid. The calculator will give you the area right away.
Base 1 (a): Type in the length of the first parallel side of the trapezoid. This is one of the two sides that run in the same direction. You can use any unit of measurement, such as inches, centimeters, or feet.
Base 2 (b): Type in the length of the second parallel side of the trapezoid. This is the other side that runs parallel to the first base. It can be longer or shorter than Base 1.
Height (h): Type in the height of the trapezoid. The height is the straight-line distance between the two parallel sides. It is not the length of a slanted side. It must be measured at a right angle to both bases.
The calculator uses the trapezoid area formula: A = ½ × (a + b) × h. It adds the two bases together, multiplies by the height, and then divides by two to find the total area in square units.
What Is a Trapezoid?
A trapezoid (called a trapezium in many countries outside the U.S.) is a four-sided flat shape with exactly one pair of parallel sides. The two parallel sides are called the bases, and the two non-parallel sides are called the legs. The height is the straight-line distance between the two bases, measured at a right angle (perpendicular) to them.
How to Find the Area of a Trapezoid
The area of a trapezoid tells you how much space the shape covers on a flat surface. The standard formula is:
Area = (a + b) × h ÷ 2
In this formula, a is the length of the top base, b is the length of the bottom base, and h is the height. You add the two bases together, multiply by the height, and then divide by 2. This works because a trapezoid is essentially the average of its two bases stretched across its height.
A Simple Example
Imagine a trapezoid where the top base (a) is 10 feet, the bottom base (b) is 16 feet, and the height (h) is 8 feet. Plug those numbers into the formula:
Area = (10 + 16) × 8 ÷ 2 = 26 × 8 ÷ 2 = 208 ÷ 2 = 104 square feet
Finding the Area from Four Side Lengths
If you know all four side lengths but not the height, you can still find the area. When the two bases have different lengths, you can use coordinate geometry to figure out the height. Place the longer base along the ground and use the leg lengths to calculate how high the top base sits above it. Specifically, if the bases are a and b and the legs are c and d, the height can be derived from:
h = √(c² − x²), where x = (c² − d² + (b − a)²) ÷ (2 × (b − a))
Once you have the height, you use the same standard area formula. This method only works when the four sides can actually form a valid trapezoid. If the legs are too short compared to the difference in base lengths, no trapezoid is possible.
Other Useful Trapezoid Measurements
- Perimeter: The total distance around the trapezoid. Add all four sides together: P = a + b + c + d.
- Median (Midsegment): A line segment that connects the midpoints of the two legs. Its length equals the average of the two bases: Median = (a + b) ÷ 2. Interestingly, the area also equals the median multiplied by the height.
- Diagonals: The two line segments drawn from one corner to the opposite corner. Their lengths depend on all four sides and the height, and they are typically unequal unless the trapezoid is isosceles (meaning both legs are the same length). Diagonal lengths can be found with the law of cosines when you know two sides and the included angle.
Types of Trapezoids
- Isosceles Trapezoid: Both legs are equal in length. The diagonals are also equal, and the shape is symmetric.
- Right Trapezoid: One of the legs is perpendicular to the bases, forming two right angles. In this case, that leg is the height. A right trapezoid shares properties with a right triangle, since removing a rectangle from the shape leaves one behind.
- Scalene Trapezoid: All four sides have different lengths, with no special symmetry.
Where Trapezoids Show Up in Real Life
Trapezoids appear more often than you might think. Cross-sections of drainage ditches, the side view of a handbag, roof gable ends, and certain bridge supports are all trapezoidal. Architects, builders, and engineers regularly calculate trapezoid areas when figuring out material costs, land areas, or structural loads. Even in math class, the trapezoid area formula is one of the most commonly tested geometry skills.