Trapezoid Calculator

Calculate the area, perimeter, angles, and diagonals of any trapezoid (also known as a trapezium). Enter the lengths of the four sides and the height (if known).

Trapezoid Formulas and Definitions

A trapezoid (or trapezium) is a quadrilateral with at least one pair of parallel sides. These parallel sides are called the bases ($a$ and $b$).

Area and Perimeter Formulas

• Area (A): The area is the average of the two parallel bases multiplied by the perpendicular height.
  $$ A = \frac{a + b}{2} \cdot h $$
• Perimeter (P): The perimeter is the sum of all four side lengths.
  $$ P = a + b + c + d $$

Types of Trapezoids

• Isosceles Trapezoid: The non-parallel sides ($c$ and $d$) are equal in length ($c=d$). The base angles are also equal ($\alpha = \delta$ and $\beta = \gamma$).
• Right Trapezoid: Has at least two right angles (90°). This occurs when one of the non-parallel sides ($c$ or $d$) is perpendicular to the parallel bases.
• Scalene Trapezoid: All four sides are of different lengths.

Frequently Asked Questions (FAQ)

What is the formula for the area of a trapezoid?

The area formula is: $A = \\frac{a + b}{2} \\cdot h$, where $a$ and $b$ are the parallel bases and $h$ is the height.

How do you find the height of a trapezoid?

If the height ($h$) is not given, it can be calculated using trigonometry or the Pythagorean theorem after splitting the trapezoid into a rectangle and one or two right triangles. This requires knowing the length of all four sides.

What is the sum of the angles in a trapezoid?

Like all quadrilaterals, the sum of the interior angles in any trapezoid is always **360 degrees**.

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A = \frac{a + b}{2} \cdot h

P = a + b + c + d

$ A = \frac{a + b}{2} \cdot h $

$ P = a + b + c + d $