Rhombus Study Guide

Definition:

A rhombus is a quadrilateral with four sides of equal length and opposite angles that are equal.

Key Properties:

All sides are of equal length
Opposite angles are of equal measure
Diagonals bisect each other at right angles
It is a type of parallelogram with additional properties

Formulas:

Area of a rhombus: A = (diagonal₁ * diagonal₂) / 2

Perimeter of a rhombus: P = 4 * side length

How to Identify:

To identify a rhombus, look for a quadrilateral with all sides of equal length and opposite angles of equal measure. It can also be identified by its diagonals intersecting at right angles.

Examples:

Example 1: Given side length = 6 units, find the area and perimeter of the rhombus.

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

Perimeter = 4 * 6 = 24 units

Example 2: In a rhombus, if one angle is 120 degrees, what is the measure of each of the other three angles?

Since opposite angles in a rhombus are equal, each of the other three angles will also be 120 degrees.

◂Math Worksheets and Study Guides Fourth Grade. Pattern Blocks

The resources above cover the following skills:

Number and Operations (NCTM)

Understand numbers, ways of representing numbers, relationships among numbers, and number systems.

Develop understanding of fractions as parts of unit wholes, as parts of a collection, as locations on number lines, and as divisions of whole numbers.

Algebra (NCTM)

Use mathematical models to represent and understand quantitative relationships.

Model problem situations with objects and use representations such as graphs, tables, and equations to draw conclusions.