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Home » Math & Conversions » Geometry » Trapezoid Calculator 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). 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: Calculate Trapezoid Properties Results Area (A) Perimeter (P) Height (h) Trapezoid Type Angles and Diagonals Angle α (Base a, Left) Angle β (Base b, Left) Angle γ (Base b, Right) Angle δ (Base a, Right) 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**. Related Calculators Solid Geometry Calculator (All Shapes) ellipse Triangle cylinder Chord Length angle central angle Midpoint pentagon Cone Volume
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