Area is the measurement of the size of a surface or a two-dimensional shape. It is the amount of space inside the boundary of a flat (2-dimensional) object such as a square, a triangle, or a circle. The formula for finding the area of different shapes varies depending on the shape you are working with.

**Rectangle:**The area of a rectangle is found by multiplying the length by the width:**Square:**The area of a square is found by squaring the length of one of its sides:**Triangle:**The area of a triangle is found using the formula:**Circle:**The area of a circle is found using the formula:

Area = side × side or Area = side^{2}

Area = π × radius^{2}

Area is typically measured in square units. Common units for measuring area include square inches (in^{2}), square feet (ft^{2}), square meters (m^{2}), etc. When calculating area, it's important to include the appropriate unit in your final answer.

Let's try solving a few practice problems to reinforce the concept of area.

- Calculate the area of a rectangle with a length of 8 units and a width of 5 units.
- Find the area of a square with a side length of 6 units.
- Determine the area of a triangle with a base of 10 units and a height of 4 units.
- Calculate the area of a circle with a radius of 3 units (use π ≈ 3.14).

Answer: Area = 8 × 5 = 40 square units

Answer: Area = 6 × 6 = 36 square units

Answer: Area = 1/2 × 10 × 4 = 20 square units

Area is a fundamental concept in geometry, and understanding how to calculate the area of different shapes is essential for solving various mathematical and real-world problems. By using the appropriate formulas and units, you can accurately determine the amount of space enclosed by different shapes.

Remember to practice calculating areas of different shapes and units to solidify your understanding of this important concept.

Study GuideMeasurement, Perimeter, and Circumference Worksheet/Answer key

Measurement, Perimeter, and Circumference Worksheet/Answer key

Measurement, Perimeter, and Circumference Worksheet/Answer key

Measurement, Perimeter, and Circumference

Geometry (NCTM)

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

Use geometric models to represent and explain numerical and algebraic relationships.

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.

Connections to the Grade 7 Focal Points (NCTM)

Measurement and Geometry: Students connect their work on proportionality with their work on area and volume by investigating similar objects. They understand that if a scale factor describes how corresponding lengths in two similar objects are related, then the square of the scale factor describes how corresponding areas are related, and the cube of the scale factor describes how corresponding volumes are related. Students apply their work on proportionality to measurement in different contexts, including converting among different units of measurement to solve problems involving rates such as motion at a constant speed. They also apply proportionality when they work with the circumference, radius, and diameter of a circle; when they find the area of a sector of a circle; and when they make scale drawings.