The longer diagonal of a kite is called the main diagonal and the shorter one is called the cross diagonal. The main diagonal of a kite is the perpendicular bisector of the cross diagonal.
That is, here the diagonal perpendicularly bisects the diagonal .
In kite , is the main diagonal. If units and units what is the length ?
Here, is the perpendicular bisector of . Then, and .
is a right triangle, units, units. Use the Pythagorean Theorem to find the length of the hypotenuse.
The opposite angles at the ends of the cross diagonal are congruent.
That is, .
The area of a kite is half the product of the lengths of the diagonals.
That is, if the lengths of the diagonals of a kite are and respectively, then area of the kite is given by the formula:
In kite , the length of the main diagonal is units and that of the cross diagonal is units. What is the area of the kite ?
Therefore, the area of the kite is square units.