Area of a Trapezoid Calculator
Calculate the area and perimeter of a trapezoid from its two parallel bases and height. See also Area of Rectangle Calculator and Area of Parallelogram Calculator.
How to Calculate the Area of a Trapezoid
A trapezoid (or trapezium) has two parallel sides called bases and two non-parallel sides called legs. To find the area, add the two bases together, multiply by the height (the perpendicular distance between the bases), and divide by 2. If you also know the leg lengths, you can calculate the perimeter by adding all four sides.
Trapezoid Area Formula
A = ½ × (a + b) × h
Perimeter = a + b + side₁ + side₂
Where a and b are the parallel bases and h is the perpendicular height between them.
Example
Find the area of a trapezoid with bases 8 and 12, height 5:
A = ½ × (a + b) × h
A = ½ × (8 + 12) × 5
A = ½ × 20 × 5
A = 50 square units
Trapezoid Area Reference Table
| Base a | Base b | Height | Area |
|---|---|---|---|
| 3 | 5 | 2 | 8.00 |
| 4 | 6 | 3 | 15.00 |
| 5 | 8 | 4 | 26.00 |
| 6 | 10 | 5 | 40.00 |
| 8 | 12 | 5 | 50.00 |
| 10 | 14 | 6 | 72.00 |
| 10 | 16 | 7 | 91.00 |
| 12 | 18 | 8 | 120.00 |
| 15 | 20 | 10 | 175.00 |
| 20 | 30 | 12 | 300.00 |
Frequently Asked Questions
What is a trapezoid?
A trapezoid (called a trapezium in British English) is a quadrilateral with exactly one pair of parallel sides. The parallel sides are called bases, and the non-parallel sides are called legs.
What is an isosceles trapezoid?
An isosceles trapezoid has legs of equal length. Its base angles are equal, and its diagonals are equal in length. The area formula is the same: A = ½(a+b)h.
How do I find the height if I only know the sides?
If you know all four sides of a trapezoid, you can find the height using the formula: h = √(c² − ((b−a)² + c² − d²)/(2(b−a)))²), where c and d are the legs. For an isosceles trapezoid: h = √(c² − ((b−a)/2)²).
Is a rectangle a special trapezoid?
Depending on the definition used, yes. Under the inclusive definition (at least one pair of parallel sides), a rectangle is a special trapezoid where both pairs of sides are parallel and all angles are 90°.