Skip to main content
math

Trapezoid Calculator

Calculate the area of a trapezoid using the two parallel sides (bases) and the height.

By Christopher FloiedPublished Updated

Length of the first parallel side

Length of the second parallel side

Minimum: 0

Perpendicular distance between the two bases

Results

Area

32 sq units

How to Use This Calculator

1

Enter your input values

Fill in all required input fields for the Trapezoid Calculator. Follow the units and input format printed next to each field. Where a unit selector is available, choose the units that match your data.

2

Review your inputs

Double-check that all values are correct and match the units or format shown for each field. Incorrect units are the most common source of calculation errors and can produce results that are off by factors of 2, 10, or more.

3

Read the results

The Trapezoid Calculator computes the output in your browser and displays the results, with units clearly labeled, as soon as they are ready — no data sent to a server.

4

Explore parameter sensitivity

Try adjusting individual input values to see how the output changes. This is a quick and effective way to develop intuition about how different parameters influence the result and to identify which inputs have the largest effect.

When to Use This Calculator

  • •Use the Trapezoid Calculator when you need a quick mathematical result without writing out all the steps manually, saving time on repetitive calculations.
  • •Use it to verify hand calculations on tests or assignments and catch arithmetic mistakes.
  • •Use it when teaching or explaining mathematical concepts to others, demonstrating how changing inputs affects the result.
  • •Use it to explore the behavior of mathematical functions across a range of inputs.

Related Calculators

Scalene Triangle Area Calculator

Calculate the area of any triangle from its three side lengths using Heron's formula. Enter sides a, b, and c to compute the area without needing height or angles, perfect for surveying, land measurement, navigation, and general geometry problems.

Circumscribed Circle (Circumradius) Calculator

Calculate the circumradius (radius of the circumscribed circle) of a triangle given its three sides using R = abc/(4*Area). The circumscribed circle passes through all three vertices. Used in geometry, trigonometry, navigation, and satellite positioning.

Equilateral Triangle Calculator

Calculate the area, perimeter, and height of an equilateral triangle from its side length.

Isosceles Triangle Calculator

Calculate the area, perimeter, and height of an isosceles triangle from its equal side and base.

Kite Area Calculator

Calculate the area of a kite from its two diagonals using A = d1*d2/2. A kite has two pairs of adjacent equal sides and perpendicular diagonals. Enter both diagonal lengths to compute the enclosed area for geometry, design, and construction projects.

Parallelogram Area Calculator

Calculate the area of a parallelogram using base times height (A = b*h). Enter the base length and the perpendicular height to find the area of this fundamental quadrilateral shape used in geometry, physics, architecture, and vector mathematics.

About Trapezoid Calculator

A trapezoid (known as a trapezium in British English) is a quadrilateral with exactly one pair of parallel sides, called the bases. The area of a trapezoid is calculated using the formula A = ½(a + b)h, where a and b are the lengths of the two parallel sides and h is the perpendicular distance between them. This formula represents the average of the two bases multiplied by the height. Trapezoids appear frequently in architecture, engineering, and everyday objects — from bridge cross-sections to lamp shades to the side view of a bucket. The trapezoidal rule in numerical analysis uses this shape to approximate areas under curves, making it fundamental to applied mathematics. This calculator provides accurate area computations for any trapezoid when you know both bases and the height.

The Math Behind It

The trapezoid area formula A = ½(a + b)h can be understood as the area of a rectangle with width h and length equal to the average of the two bases, (a + b)/2. This is called the midsegment or median of the trapezoid. The formula can also be derived by dividing the trapezoid into two triangles sharing the same height: one with base a and one with base b, giving total area ½ah + ½bh = ½(a + b)h. An isosceles trapezoid has equal non-parallel sides (legs) and equal base angles. For an isosceles trapezoid, the diagonals are equal in length. The trapezoidal rule in calculus approximates ∫f(x)dx by dividing the interval into n strips, each approximated as a trapezoid: ∫ₐᵇ f(x)dx ≈ (h/2)[f(x₀) + 2f(x₁) + ... + 2f(xₙ₋₁) + f(xₙ)]. This method has error of order O(h²), making it more accurate than the left or right Riemann sum.

Formula Reference

Trapezoid Area

A = ½ × (a + b) × h

Variables: a, b = parallel sides (bases), h = height

Worked Examples

Example 1: Cross-section of a ditch

A ditch has a top width of 3 m, bottom width of 1.5 m, and depth of 1.2 m.

Step 1:A = ½ × (3 + 1.5) × 1.2
Step 2:A = ½ × 4.5 × 1.2
Step 3:A = ½ × 5.4

A = 2.7 square meters

Common Mistakes & Tips

  • !Using a slant side length instead of the perpendicular height.
  • !Forgetting to average the two bases (dividing by 2).
  • !Assuming the formula works for shapes with no parallel sides — it requires exactly one pair of parallel sides.

Related Concepts

Area of a Rectangle

A rectangle is a special trapezoid where both bases are equal.

Area of a Triangle

A triangle is a degenerate trapezoid where one base has length zero.

Frequently Asked Questions

What is the difference between a trapezoid and a parallelogram?

A trapezoid has exactly one pair of parallel sides, while a parallelogram has two pairs. A parallelogram can be seen as a special trapezoid.

What is the trapezoidal rule?

The trapezoidal rule is a method of numerical integration that approximates the area under a curve by dividing it into trapezoids. It uses the same area formula as this calculator.

Add the live Trapezoid Calculator to your site. Free to embed, with a link back to MegaCalc.