A Guide to the GRE/Kites

= Kites =

Rules
The diagonals of a kite are perpendicular, and its area is the product of these diagonals.

A kite has two pairs of adjacent equal sides.

Its diagonals form right angles, which, if multiplied, yield the area of the kite. Because the diagonals are perpendicular, the perimeter of a kite can be determined using the 					      Pythagorean Theorem.

Practice
1. In figure JKLM, sides JK and KL are equal, and sides LM and MJ are equal. The distance from K to M is twice the distance from J to L. If the area of JKLM is 50, what is the distance from K to M?

2. The lengths of both NO and NQ are 52, while the lengths of both OP and PQ are 25. If the distance from O to Q is 40, what is the distance from N  to P?

Answers to Practice Questions
1. 10

The area of a kite equals the product of its diagonals. Since the area of this kite is 50 and one diagonal is half the length of the other, the lengths can be determined using algebra. Let d equal the smaller diagonal.

d(2d) = 50		Take the initial equation.

2d2 = 50		Expand the parentheses.

d2 = 25			Divide both sides by 2.

d = 5			Take the square root of both sides. The smaller diagonal 			is equal to 5, making the larger one 10.

2. 63

The kite can be split into four different right triangles. The missing sides when combined form the unknown diagonal, which pursuant to the Pythagorean Theorem can be calculated as +, or 48 + 15, which equals 63.