Trapezoid Calculator

Calculate all properties of a trapezoid including area, perimeter, median, and diagonals. Works with both isosceles and scalene trapezoids.

Length of the first parallel side

Length of the second parallel side

Perpendicular distance between the two bases

Length of first non-parallel side (optional)

Length of second non-parallel side (optional)

Area = ((a + b) / 2) * h Perimeter = a + b + c + d Median = (a + b) / 2 Leg (isosceles) = sqrt(h^2 + ((a-b)/2)^2) Diagonal (isosceles) = sqrt(leg^2 + a*b) Where: a, b = parallel bases h = height (perpendicular distance) c, d = legs (non-parallel sides)
Example 1 (Isosceles Trapezoid): Base 1 = 10 cm Base 2 = 6 cm Height = 4 cm Area = (10+6)/2 * 4 = 32 cm^2 Perimeter = 10 + 6 + 4.47 + 4.47 = 24.94 cm Median = (10+6)/2 = 8 cm Leg = sqrt(4^2 + 2^2) = 4.47 cm Example 2 (Garden Bed): Base 1 = 15 ft Base 2 = 10 ft Height = 8 ft Area = (15+10)/2 * 8 = 100 ft^2 Perimeter = 15 + 10 + 8.08 + 8.08 = 41.16 ft Median = 12.5 ft

What is a trapezoid?

A trapezoid (or trapezium in British English) is a quadrilateral with at least one pair of parallel sides. The parallel sides are called bases (base a and base b), and the non-parallel sides are called legs. An isosceles trapezoid has equal leg lengths.

What is the formula for the area of a trapezoid?

The area of a trapezoid is: Area = (1/2) * (base₁ + base₂) * height, or Area = ((a + b)/2) * h. This is the average of the two bases multiplied by the height. For bases of 10 cm and 6 cm with height 5 cm: Area = (10 + 6)/2 * 5 = 40 cm^2.

How do I calculate the perimeter of a trapezoid?

The perimeter is the sum of all four sides: Perimeter = base₁ + base₂ + leg₁ + leg₂. For an isosceles trapezoid (equal legs), it simplifies to: Perimeter = base₁ + base₂ + 2 * leg.

What is the height of a trapezoid?

The height (or altitude) is the perpendicular distance between the two parallel bases. It is not the same as the leg length unless the trapezoid is a rectangle. The height is essential for calculating the area.

What is the median (mid-segment) of a trapezoid?

The median (or midsegment) is a line segment connecting the midpoints of the two legs. Its length equals the average of the two bases: Median = (base₁ + base₂)/2. The median is always parallel to the bases.

How do I find the leg length of an isosceles trapezoid?

For an isosceles trapezoid, you can use the Pythagorean theorem. If you know the bases and height: leg = sqrt(h^2 + ((b₁ - b₂)/2)^2), where h is height, and b₁ and b₂ are the bases. Each leg has the same length in an isosceles trapezoid.

What is the difference between a trapezoid and a parallelogram?

A trapezoid has one pair of parallel sides, while a parallelogram has two pairs of parallel sides. All parallelograms are trapezoids (by the inclusive definition), but not all trapezoids are parallelograms. A rectangle is both.

What are real-world applications of trapezoid calculations?

Trapezoids are used in: architectural design (trapezoidal windows and roofs), bridge construction (trapezoidal supports), furniture design (table legs), landscaping (garden beds), roadway design (cross-sections), and various engineering structures.

Can a trapezoid have right angles?

Yes! A right trapezoid has two right angles (90deg) adjacent to one of the legs. This makes one leg perpendicular to both bases, and that leg length equals the height of the trapezoid.

How do I calculate a trapezoid if I only know the area and one base?

You need at least two of these three measurements: both bases, height, or area. With area and one base, you also need the height to find the other base: base₂ = (2 * Area)/height - base₁.