Quadrilateral Calculator

Calculate area, perimeter, and properties of any quadrilateral using four sides and a diagonal.

Enter Quadrilateral Dimensions

Enter four consecutive sides and the diagonal connecting vertices 1 and 3. Sides go around the quadrilateral in order: a (1-2), b (2-3), c (3-4), d (4-1).

Result

Area
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square units

Step-by-Step Solution

Area via triangulation: A = A1 + A2

Understanding Quadrilaterals

A quadrilateral is a polygon with four sides, four vertices, and four angles. The sum of interior angles in any quadrilateral is 360 degrees. Quadrilaterals come in many forms, from regular shapes like squares to irregular general quadrilaterals.

Types of Quadrilaterals

Square

All sides equal, all angles 90 degrees. A regular quadrilateral.

A = a², P = 4a

Rectangle

Opposite sides equal, all angles 90 degrees.

A = l x w, P = 2(l + w)

Parallelogram

Opposite sides parallel and equal. Opposite angles equal.

A = b x h

Rhombus

All sides equal. Opposite angles equal. Diagonals bisect each other at right angles.

A = (d1 x d2) / 2

Trapezoid

Exactly one pair of parallel sides.

A = (a + b) x h / 2

General Quadrilateral

Any four-sided polygon. Use triangulation or Bretschneider's formula.

A = sqrt((s-a)(s-b)(s-c)(s-d) - abcd*cos²(theta))

Calculation Methods

Triangulation Method

A diagonal divides the quadrilateral into two triangles. The area of each triangle is computed using Heron's formula, and the total area is their sum. This is the most straightforward method when a diagonal is known.

Bretschneider's Formula

For a general quadrilateral with sides a, b, c, d and diagonals p, q, Bretschneider's formula generalizes Heron's formula. It requires knowledge of opposite angles or both diagonals.

Tips

  • The triangle inequality must hold for both triangles formed by the diagonal.
  • The diagonal must be shorter than the sum of the two sides it connects.
  • For cyclic quadrilaterals, use Brahmagupta's formula: A = sqrt((s-a)(s-b)(s-c)(s-d)).
  • Interior angles always sum to 360 degrees.