Look a little closer.

A diagonal is the key to this symmetry. These connections help explain why the figure behaves as it does, beyond simply entering numbers into a formula.

01 / A useful relationship

One pair of opposite angles is equal.

Its symmetry diagonal bisects the crossing diagonal at a right angle. The two segments of the symmetry diagonal need not be equal. Area is half the product of the perpendicular diagonals.

02 / A different perspective

The two triangles on either side of the symmetry diagonal are mirror images.

A convex kite has two pairs of adjacent equal sides. We use the symmetric convex form, including a rhombus as a special case. Concave arrowhead or dart shapes are outside these calculators.

03 / A connection to explore

Both diagonals are bisected only in the rhombus special case.

Use both diagonal lengths for area. To obtain side-based perimeter as well, give the adjacent side-pair lengths and the crossing diagonal, or give the two symmetry-diagonal segments with the crossing diagonal.

Try the idea with numbers

Open the perpendicular diagonals calculator, note its outputs, then multiply each length input by two. Area should increase by four and every reported length should double, when every relevant length is doubled. Angle inputs and dimensionless ratios remain unchanged. This scaling experiment checks the structure of the formula rather than the precision of any real measurement.

Further reading: Kite at Wolfram MathWorld.