What is an isosceles trapezoid?

An isosceles trapezoid is a trapezoid where the non-parallel sides (legs) are equal in length. This also means that the base angles (angles on the same base) are equal.

Trapezoid Calculator

Q: 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.

Q: How do you find the height of a trapezoid?

If you know the lengths of all four sides ($a, b, c, d$), the height ($h$) can be found by splitting the trapezoid into a rectangle and two right triangles and using the Pythagorean theorem, which can be complex. Our calculator does this for you automatically.

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).

Input Parameters

Base a (Top parallel side):

Base b (Bottom parallel side):

Side c (Left oblique side):

Side d (Right oblique side):

Height h (Perpendicular):

Decimal Precision:

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**.