How this calculator works
A kite has two adjacent pairs of equal sides. Its perpendicular diagonals split its area into four right triangles, giving half their product. Alternatively, the symmetry diagonal splits it into two congruent triangles with sides a and b and included angle α. Doubling the triangle sine-area formula gives ab sin α. Diagonals alone do not fix the perimeter because their intersection position is unknown. Side-angle entries must form a convex kite. In reverse angle mode, a supplementary candidate is reported only if it also leaves both symmetry-axis corners convex.
Formula
K=ef/2; missing f=2K/e; K=ab sin α; P=2(a+b). For known K≤ab, test α=arcsin(K/ab) and 180°-arcsin(K/ab); convexity requires cos α < min(a/b,b/a).
Worked example
Diagonals of 6 m and 8 m enclose 24 m². A side pair of 3 m and 5 m meeting at 90° gives 15 m² and perimeter 16 m. Area 7.5 m² with those sides gives a convex kite at 150°; the 30° sine solution would form a concave dart.
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Frequently asked questions
Which angle goes with the side formula?
Use an angle where a side from each equal pair meets. An angle between two equal sides needs a different construction.
Can the area exceed ab?
No. The sine is at most one, so the maximum is ab at a 90° included angle.
Why are there two possible angles?
Supplementary angles have equal sines. Both are returned only when both shapes are convex kites; otherwise only the valid convex angle is shown.