In geometry, the area of a 2D shape refers to the amount of space it occupies. The area of triangles and quadrilaterals can be calculated using specific formulas based on their respective shapes.

The formula to calculate the area of a triangle is:

Where the base is the length of the triangle's bottom side, and the height is the perpendicular distance from the base to the opposite vertex.

Calculate the area of a triangle with a base of 6 units and a height of 4 units.

Area = 1/2 * 6 * 4 = 12 square units

The formula for finding the area of a quadrilateral depends on its shape. For rectangles and squares, the formula is:

For other quadrilaterals, such as parallelograms or trapezoids, the formula is:

Area = 1/2 * (sum of parallel sides) * height

Where the height is the perpendicular distance between the two parallel sides.

Calculate the area of a rectangle with a length of 8 units and a width of 5 units.

Area = 8 * 5 = 40 square units

Study GuideArea of Triangles and Quadrilaterals Activity LessonArea and Volume Activity LessonArea of Triangles Worksheet/Answer key

Area of Triangles and Quadrilaterals Worksheet/Answer key

Area of Triangles and Quadrilaterals Worksheet/Answer key

Area of Triangles and Quadrilaterals Worksheet/Answer keyIdentifying Triangles Worksheet/Answer keyTriangle Inequality Theorem Worksheet/Answer keyIdentifying Triangles Worksheet/Answer keyTriangle Inequality Theorem Vocabulary/Answer keyArea of Triangles and Quadrilaterals Vocabulary/Answer keyArea of Triangles and Quadrilaterals

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 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.