Kite Study Guide

Definition

A kite in geometry is a quadrilateral with two distinct pairs of adjacent sides that are congruent. This means that the sides next to each other are of equal length.

Properties of a Kite

• A kite has two distinct pairs of adjacent sides that are congruent.
• One pair of opposite angles in a kite are congruent.
• The diagonals of a kite are perpendicular to each other.
• The longer diagonal of a kite bisects the shorter diagonal, creating two right angles.

Formulas

Area of a kite: A = (1/2) * d1 * d2, where d1 and d2 are the lengths of the diagonals.

Example Problems

Problem 1

Find the area of a kite with diagonals of length 8 cm and 10 cm.

Using the formula, A = (1/2) * d1 * d2, we get A = (1/2) * 8 * 10 = 40 square cm.

Problem 2

If a kite has a longer diagonal of 16 cm and a shorter diagonal of 12 cm, find the area.

Using the same formula, A = (1/2) * d1 * d2, we get A = (1/2) * 16 * 12 = 96 square cm.

Conclusion

A kite is a special quadrilateral with unique properties and formulas for calculating its area. Understanding the properties and formulas related to kites can help in solving geometry problems efficiently.