Definition of Area and Perimeter

Area is the measure of the amount of space enclosed within a 2-dimensional shape. Perimeter is the distance around the boundary of a 2-dimensional shape.

Formulas

For a rectangle:

Area = length × width
Perimeter = 2 × (length + width)

For a square:

Area = side × side
Perimeter = 4 × side

For a triangle:

Area = 0.5 × base × height
Perimeter = side1 + side2 + side3

For a circle:

Area = π × radius × radius
Perimeter (also known as circumference) = 2 × π × radius

Examples

Example 1: Find the area and perimeter of a rectangle with length 5 cm and width 3 cm.

Area = 5 cm × 3 cm = 15 cm²

Perimeter = 2 × (5 cm + 3 cm) = 2 × 8 cm = 16 cm

Example 2: Find the area and perimeter of a square with side length 7 cm.

Area = 7 cm × 7 cm = 49 cm²

Perimeter = 4 × 7 cm = 28 cm

Example 3: Find the area and perimeter of a triangle with base 6 cm and height 4 cm.

Area = 0.5 × 6 cm × 4 cm = 12 cm²

Perimeter = side1 + side2 + side3 = (To be calculated using the given side lengths)

Study Guide

1. Understand the difference between area and perimeter.

2. Memorize the formulas for calculating the area and perimeter of rectangles, squares, triangles, and circles.

3. Practice solving problems involving the calculation of area and perimeter for different shapes.

4. Learn how to apply the formulas to real-life situations, such as calculating the area of a room or the perimeter of a garden.

By understanding the concepts and practicing the calculations, you can become proficient in finding the area and perimeter of various shapes.

◂Math Worksheets and Study Guides Fourth Grade. Area and Perimeter

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.

Grade 4 Curriculum Focal Points (NCTM)

Measurement: Developing an understanding of area and determining the areas of two-dimensional shapes

Students recognize area as an attribute of two-dimensional regions. They learn that they can quantify area by finding the total number of same-sized units of area that cover the shape without gaps or overlaps. They understand that a square that is 1 unit on a side is the standard unit for measuring area. They select appropriate units, strategies (e.g., decomposing shapes), and tools for solving problems that involve estimating or measuring area. Students connect area measure to the area model that they have used to represent multiplication, and they use this connection to justify the formula for the area of a rectangle.

Connections to the Grade 4 Focal Points (NCTM)

Geometry: Students extend their understanding of properties of two-dimensional shapes as they find the areas of polygons. They build on their earlier work with symmetry and congruence in grade 3 to encompass transformations, including those that produce line and rotational symmetry. By using transformations to design and analyze simple tilings and tessellations, students deepen their understanding of two-dimensional space.