Free · Mathematical relations and geometry

Kite Area and Paired-Side Perimeter

Calculate a kite’s area from perpendicular diagonals or adjacent unequal sides and their included angle.

Calculator inputs

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Enter the known values in the units shown. Results update as you type.
Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
Use the worked example to check the method. Reset restores the starting fields.

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Perpendicular diagonals 6 and 8 give kite area 24. Adjacent sides 3 and 4 enclosing 90° give area 12 and perimeter 14.

A=ef/2; A=ab sin θ; P=2(a+b)

Enter these known values and leave the other values blank.

A kite has two pairs of adjacent equal sides and perpendicular diagonals.
The SAS angle is between two unequal adjacent sides. Doubling the congruent-triangle area yields ab sin θ.
Perimeter is twice the sum of the two distinct adjacent side lengths; diagonals alone do not uniquely determine it.
All lengths and areas are positive. An angle inverse selects the acute principal branch; the supplementary angle produces the same area.

Leave the unknown control empty and enter the quantities needed by the selected relation. Read the assumptions for any branch or domain restrictions.

It is an exact mathematical model with independently checked numbers. Display rounding does not change the values used for subsequent calculations.

The international acre is exactly 43560 square international feet; Bookify replaces the rounded captured area factor.