How this calculator works
Two diagonals and their included angle give half their cross product. Bimedians connect opposite side midpoints; their cross product gives the full quadrilateral area, with no factor of one half. Opposite-angle mode splits a convex outline along AC and checks that both triangles imply the same diagonal. Coordinate mode sums translated shoelace terms and rejects crossing sides. Perimeter appears only when the inputs determine it. Coordinate entries use metres, so their area and perimeter use the same unit controls as the other methods.
Formula
Diagonals: K=pq sin(θ)/2. Bimedians: K=mn sin(θ). Opposite angles: K=[ab sin(B)+cd sin(D)]/2, subject to matching AC. Coordinates: K=|Σ(xᵢyᵢ₊₁-yᵢxᵢ₊₁)|/2.
Worked example
A 3 m by 4 m rectangle has diagonals of length 5 m with sin(θ)=24/25, giving K=12 m². Its perpendicular bimedians are 3 m and 4 m, also giving 12 m², without the diagonal formula’s factor of one half.
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Frequently asked questions
What is a bimedian?
It joins the midpoints of two opposite sides. It is different from a diagonal, which joins opposite vertices.
Can I enter a concave quadrilateral?
Use ordered coordinates for a simple concave outline. Opposite-angle and diagonal measurement modes assume the convex case.
Why do some modes omit perimeter?
Diagonals, bimedians, or a base and height can leave side lengths undetermined. An area calculation alone cannot justify a perimeter.