Perimeter Study Guide

Perimeter is the distance around the outside of a shape. It is the sum of all the side lengths of the shape.

Formulas for Calculating Perimeter

Here are the formulas for calculating the perimeter of different shapes:

Rectangle: Perimeter = 2 * (length + width)
Square: Perimeter = 4 * side length
Triangle: Perimeter = sum of all three sides
Circle: Perimeter = 2 * π * radius (or π * diameter)

Example Problems

Let's solve some example problems to practice calculating perimeter:

Find the perimeter of a rectangle with a length of 8 units and a width of 5 units.
Perimeter = 2 * (8 + 5) = 2 * 13 = 26 units
What is the perimeter of a square with a side length of 10 inches?
Perimeter = 4 * 10 = 40 inches
Determine the perimeter of a triangle with side lengths of 7 cm, 9 cm, and 12 cm.
Perimeter = 7 + 9 + 12 = 28 cm
Calculate the perimeter of a circle with a radius of 5 meters. (Use π ≈ 3.14)
Perimeter = 2 * 3.14 * 5 = 31.4 meters

Summary

Perimeter is the total distance around the boundary of a shape. To find the perimeter, add up all the side lengths of the shape. Use the appropriate formula for different shapes, such as rectangles, squares, triangles, and circles.

◂Math Worksheets and Study Guides Sixth Grade. Formulas

Study Guide

Formulas

Activity Lesson

Equivalent Expressions (Distributive Property)

The resources above cover the following skills:

Algebra (NCTM)

Use mathematical models to represent and understand quantitative relationships.

Model and solve contextualized problems using various representations, such as graphs, tables, and equations.

Measurement (NCTM)

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

Select and apply techniques and tools to accurately find length, area, volume, and angle measures to appropriate levels of precision.

Develop and use formulas to determine the circumference of circles and the area of triangles, parallelograms, trapezoids, and circles and develop strategies to find the area of more-complex shapes.

Grade 6 Curriculum Focal Points (NCTM)

Algebra: Writing, interpreting, and using mathematical expressions and equations

Students write mathematical expressions and equations that correspond to given situations, they evaluate expressions, and they use expressions and formulas to solve problems. They understand that variables represent numbers whose exact values are not yet specified, and they use variables appropriately. Students understand that expressions in different forms can be equivalent, and they can rewrite an expression to represent a quantity in a different way (e.g., to make it more compact or to feature different information). Students know that the solutions of an equation are the values of the variables that make the equation true. They solve simple one-step equations by using number sense, properties of operations, and the idea of maintaining equality on both sides of an equation. They construct and analyze tables (e.g., to show quantities that are in equivalent ratios), and they use equations to describe simple relationships (such as 3x = y) shown in a table.

Connections to the Grade 6 Focal Points (NCTM)

Measurement and Geometry: Problems that involve areas and volumes, calling on students to find areas or volumes from lengths or to find lengths from volumes or areas and lengths, are especially appropriate. These problems extend the students' work in grade 5 on area and volume and provide a context for applying new work with equations.