Perimeter Quadrilateral Calculator

Background.

Going around the outside of a four-sided shape is the easy part: add the four sides. A fence line, a run of skirting board, the edging for an oddly shaped flower bed — the perimeter needs nothing more, whatever the angles at the corners. The area is a different matter, and it is the reason this page asks for one extra measurement.

Four side lengths do not pin down a quadrilateral. Join four sticks of 3, 4, 3 and 4 at the corners with loose pins and they can form a 3-by-4 rectangle, or you can push the frame over into a leaning parallelogram, or squash it almost flat. The perimeter stays 14 throughout, but the area slides from 12 down towards zero. Triangles do not behave like this — three sides fix a triangle completely — so the standard remedy is to measure one diagonal too, which splits the shape into two triangles whose shapes are then locked.

Each triangle's area follows from its three sides by Heron's formula, which needs no angles or heights, and the two areas add. That makes the method practical with nothing but a tape: measure the four boundaries of a plot or a room and one corner-to-corner line, and you have the area without a protractor.

Two conditions matter. The diagonal must be the one that separates sides a and b from sides c and d, and each triangle it creates must be possible — the diagonal shorter than the two sides beside it combined, and longer than their difference. And if one corner of the shape points inwards, measure the diagonal that runs inside it, because the two triangle areas are always added, never subtracted.

What is perimeter quadrilateral calculator?

A quadrilateral is any closed four-sided figure: square, rectangle, kite, trapezium or something entirely irregular. Its perimeter is the total length of its boundary, a + b + c + d, in the same unit as the sides. Its area is the space it encloses, in square units. The side lengths alone fix the perimeter but not the area, which is why a diagonal is entered as well. A diagonal joins two opposite corners and divides the shape into two triangles.

How to use this calculator.

1. 01Label the corners in order around the shape and enter the four sides in that order, so that sides a and b meet at one corner and sides c and d meet at the opposite corner.
2. 02Measure the diagonal joining the other two corners — the line with sides a and b on one side of it and c and d on the other — and enter it in the same unit as the sides.
3. 03If one corner is pushed inwards, use the diagonal that lies inside the shape; the outside one would make the page add a triangle of area that is not part of the shape at all.
4. 04Read the perimeter, and the area in the square of whatever unit you used: sides in metres give square metres, sides in feet give square feet.

The formula.

Perimeter = a + b + c + d. For the area, the diagonal e splits the shape into triangles with sides (a, b, e) and (c, d, e). Heron's formula gives a triangle's area from its sides alone: with the semi-perimeter s = (x + y + z) ÷ 2, the area is √(s(s − x)(s − y)(s − z)). The quadrilateral's area is the sum of the two triangles' areas. Each triangle must satisfy the triangle inequality — every side shorter than the other two combined — or there is no triangle to measure, and the page reports an error on the diagonal. The area reacts most strongly to the diagonal when one of the triangles is nearly flat, so small measuring errors matter most there. For any given four sides, the area is largest when all four corners lie on one circle, which is why the rectangle beats every leaning version of the same frame.

A worked example.

Frequently asked questions.

References& sources.

1. [1]OpenStax, Rice University. Precalculus 2e, 2021. Trigonometry and analytic geometry chapters. Retrieved 2026-08-06.
2. [2]OpenStax, Rice University. College Algebra 2e, 2021. Algebra and function chapters. Retrieved 2026-08-06.
3. [3]NIST/SEMATECH. e-Handbook of Statistical Methods, 2012. Chapter 1.3 and Chapter 4. Retrieved 2026-08-06.