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A kite is a quadrilateral with exactly two pairs of adjacent congruent sides.

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This definition excludes squares and rhombi which have all 4 side congruent.

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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 BD ¯ perpendicularly bisects the diagonal AC ¯ .

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Example 1:

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In kite PQRS , QS is the main diagonal. If PR=10 units and QO=4 units what is the length PQ ?

Here, QS is the perpendicular bisector of PR . Then, mQOP=90° and PO= 1 2 PR=RO .

PO= 1 2 ( 10 )


ΔPOQ is a right triangle, PO=5 units, QO=4 units. Use the Pythagorean Theorem to find the length of the hypotenuse.

PQ= ( PO ) 2 + ( QO ) 2

= 5 2 + 4 2

= 25+16

= 41

The opposite angles at the ends of the cross diagonal are congruent.

That is, BADBCD .

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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 d 1 and d 2 respectively, then area A of the kite is given by the formula:

A= 1 2 d 1 d 2

Example 2:

In kite LMNO , the length of the main diagonal MO is 12 units and that of the cross diagonal LN is 5 units. What is the area of the kite LMNO ?

A= 1 2 ( MO )( LN )

= 1 2 ( 12 )( 5 )

= 1 2 ( 60 )


Therefore, the area of the kite LMNO is 30 square units.

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