Trapezoid Calculator
Free Trapezoid Calculator for linear algebra. Enter values to get step-by-step solutions with formulas and graphs. See charts, tables, and visual results.
Reviewed by Manoj Kumar, Mathematics Educator
Formula
A = ((a + b) / 2) x h
Where A = Area, a = length of the first base (parallel side), b = length of the second base (parallel side), and h = perpendicular height between the two bases. The median (midsegment) equals (a + b) / 2.
Worked Examples
Example 1: Standard Trapezoid Area Calculation
Problem:Find the area, perimeter, and median of a trapezoid with bases 12 cm and 8 cm, height 5 cm, and legs 5.39 cm each.
Solution:Area = ((12 + 8) / 2) x 5 = (20 / 2) x 5 = 10 x 5 = 50 sq cm\nPerimeter = 12 + 8 + 5.39 + 5.39 = 30.78 cm\nMedian = (12 + 8) / 2 = 10 cm\nThis is an isosceles trapezoid since both legs are equal.
Result:Area: 50 sq cm | Perimeter: 30.78 cm | Median: 10 cm
Example 2: Right Trapezoid Calculation
Problem:Calculate the area and angles of a right trapezoid with bases 10 cm and 6 cm, height 4 cm, and legs 4 cm and 5.66 cm.
Solution:Area = ((10 + 6) / 2) x 4 = (16 / 2) x 4 = 8 x 4 = 32 sq cm\nLeft angle = arctan(4 / 0) = 90 degrees (right angle)\nRight angle = arctan(4 / 4) = 45 degrees\nPerimeter = 10 + 6 + 4 + 5.66 = 25.66 cm
Result:Area: 32 sq cm | Angles: 90 and 45 degrees at base
Frequently Asked Questions
What is a trapezoid and what are its defining properties?
A trapezoid (called a trapezium in British English) is a quadrilateral with exactly one pair of parallel sides. The parallel sides are called bases, while the non-parallel sides are called legs. The perpendicular distance between the two bases is the height. The midsegment (or median) connects the midpoints of the two legs and is parallel to both bases. Trapezoids appear frequently in architecture, engineering, and everyday objects such as table tops, handbags, and bridge supports. The shape is fundamental in geometry and serves as a building block for understanding more complex polygonal figures and area calculations.
How do you calculate the area of a trapezoid?
The area of a trapezoid is calculated using the formula A = ((a + b) / 2) times h, where a and b are the lengths of the two parallel bases and h is the perpendicular height between them. This formula essentially finds the average of the two bases and multiplies it by the height. You can think of it as converting the trapezoid into a rectangle with width equal to the average base length. This formula works for all types of trapezoids including right trapezoids, isosceles trapezoids, and scalene trapezoids. The area is always expressed in square units corresponding to the unit of measurement used for the sides.
What is the difference between an isosceles and a right trapezoid?
An isosceles trapezoid has two legs (non-parallel sides) of equal length, which means the base angles are also equal. This gives the shape a line of symmetry through the midpoints of the two bases. A right trapezoid has two adjacent right angles (90 degrees), meaning one of its legs is perpendicular to both bases. Isosceles trapezoids are common in decorative designs and architecture because of their symmetry, while right trapezoids frequently appear in calculus when approximating areas under curves using the trapezoidal rule. Both types are special cases of the general trapezoid and have unique geometric properties.
How do you find the diagonals of a trapezoid?
To find the diagonals of a trapezoid, you can use coordinate geometry by placing the trapezoid on a coordinate plane. Set the longer base along the x-axis, then position the shorter base parallel to it at the given height. The diagonal lengths are calculated using the distance formula between opposite vertices. In an isosceles trapezoid, both diagonals are equal in length. For a general trapezoid with bases a and b, legs c and d, and height h, the diagonals can also be found using the generalized formula involving these measurements. The diagonals of a trapezoid always intersect each other inside the figure.
References
Reviewed by Manoj Kumar, Mathematics Educator · Editorial policy