Kite - Geometry

Definition:

A kite is a quadrilateral with two distinct pairs of adjacent sides that are congruent. In other words, a kite is a shape with two pairs of adjacent sides that are equal in length.

Properties:

A kite has two distinct pairs of adjacent sides that are congruent (AB = BC and AD = DC).
The diagonals of a kite are perpendicular to each other.
One diagonal of a kite bisects the other diagonal, and vice versa.
The longer diagonal of a kite bisects the shorter diagonal into two equal segments.
The angles between the unequal sides are equal (angle A and angle C are congruent, angle B and angle D are congruent).

Formulas:

Area of a kite = (diagonal 1 * diagonal 2) / 2

Perimeter of a kite = sum of all four sides

Examples:

Example 1: Calculate the area and perimeter of a kite with diagonals of 8 cm and 6 cm.

Area = (8 * 6) / 2 = 24 square cm

Perimeter = AB + BC + CD + DA = 8 + 8 + 6 + 6 = 28 cm

Example 2: If the longer diagonal of a kite is 10 cm and it bisects the shorter diagonal into two equal segments, each segment would be 5 cm.

Example 3: In a kite ABCD, if AB = BC = 5 cm and AD = DC = 7 cm, then angle A = angle C and angle B = angle D.

Practice Problems:

1. Find the area and perimeter of a kite with diagonals of 12 cm and 8 cm.

2. If the diagonals of a kite are 15 cm and 9 cm, and one diagonal bisects the other, find the length of each segment of the shorter diagonal.

3. In a kite PQRS, if PQ = RS = 6 cm and PR = QS = 10 cm, find the measures of angles P, Q, R, and S.

◂Math Worksheets and Study Guides Fifth Grade. Area

The resources above cover the following skills:

Geometry (NCTM)

Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships.

Identify, compare, and analyze attributes of two- and three-dimensional shapes and develop vocabulary to describe the attributes.

Use visualization, spatial reasoning, and geometric modeling to solve problems.

Use geometric models to solve problems in other areas of mathematics, such as number and measurement.

Measurement (NCTM)

Understand measurable attributes of objects and the units, systems, and processes of measurement.

Understand such attributes as length, area, weight, volume, and size of angle and select the appropriate type of unit for measuring each attribute.

Apply appropriate techniques, tools, and formulas to determine measurements.

Develop, understand, and use formulas to find the area of rectangles and related triangles and parallelograms.