Pentagon

A pentagon is a five-sided polygon. The sum of the interior angles of any pentagon is always 540 degrees. Each interior angle of a regular pentagon measures 108 degrees. A regular pentagon has all its sides and angles equal in measure.

Properties of a Pentagon

A pentagon has 5 sides and 5 vertices.
The sum of the interior angles of a pentagon is given by the formula: (n-2) * 180 degrees, where n is the number of sides.
Each interior angle of a regular pentagon measures 108 degrees.
A regular pentagon has 5 equal sides and 5 equal interior angles.
The exterior angles of a pentagon add up to 360 degrees. Each exterior angle is supplementary to the interior angle.

Formulas for a Pentagon

Sum of interior angles = (n-2) * 180 degrees

Each interior angle of a regular pentagon = 108 degrees

Perimeter of a pentagon = 5 * length of one side

Area of a regular pentagon = (1/4) * sqrt(5 * (5 + 2*sqrt(5))) * s², where s is the length of a side

Example Problems

Find the sum of the interior angles of a pentagon.

Solution: Using the formula, (5-2) * 180 = 3 * 180 = 540 degrees

Find the measure of each interior angle of a regular pentagon.

Solution: Each interior angle of a regular pentagon measures 108 degrees.

Calculate the perimeter of a pentagon with a side length of 8 cm.

Solution: Perimeter = 5 * 8 = 40 cm

Determine the area of a regular pentagon with a side length of 6 units.

Solution: Area = (1/4) * sqrt(5 * (5 + 2*sqrt(5))) * 6² = 54.44 square units

Practice Problems

1. Find the measure of each interior angle of a regular pentagon.

2. Calculate the perimeter of a pentagon with a side length of 12 cm.

3. Determine the area of a regular pentagon with a side length of 10 units.

4. Find the sum of the interior angles of a pentagon.

◂Math Worksheets and Study Guides Fifth Grade. Multiplication

Vocabulary/Answer key

Multiplication

The resources above cover the following skills:

Number and Operations (NCTM)

Compute fluently and make reasonable estimates.

Develop fluency in adding, subtracting, multiplying, and dividing whole numbers.

Select appropriate methods and tools for computing with whole numbers from among mental computation, estimation, calculators, and paper and pencil according to the context and nature of the computation and use the selected method or tools.

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.

Connections to the Grade 5 Focal Points (NCTM)

Number and Operations: Building on their work in grade 4, students extend their understanding of place value to numbers through millions and millionths in various contexts. They apply what they know about multiplication of whole numbers to larger numbers. Students also explore contexts that they can describe with negative numbers (e.g., situations of owing money or measuring elevations above and below sea level).