When dealing with coordinate polygons, the area can be calculated using the formula:

**Area = 1/2 * |x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)|**

Where (x1, y1), (x2, y2), and (x3, y3) are the coordinates of the vertices of the polygon. The absolute value signs are used to ensure that the area is always positive.

- Identify the coordinates of the vertices of the polygon.
- Substitute the coordinates into the formula: Area = 1/2 * |x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)|
- Calculate the area by simplifying the expression.

Find the area of the triangle with vertices A(3, 4), B(7, 1), and C(5, 6).

Substitute the coordinates into the formula: Area = 1/2 * |3(1 - 6) + 7(6 - 4) + 5(4 - 1)|

Calculate the area: Area = 1/2 * |-15 + 14 + 15| = 1/2 * 44 = 22 square units

So, the area of the triangle is 22 square units.

- Understand the formula for finding the area of a coordinate polygon.
- Practice substituting coordinates into the formula and calculating the area.
- Work on different types of polygons such as triangles, quadrilaterals, and irregular polygons.
- Remember to use the absolute value of the expression to ensure the area is positive.

By following these steps and practicing different examples, you can master the concept of finding the area of coordinate polygons.

Good luck with your studies!

.Study GuideArea of Coordinate Polygons Activity LessonArea of Coordinate Polygons Worksheet/Answer key

Area of Coordinate Polygons Worksheet/Answer key

Area of Coordinate Polygons Worksheet/Answer key

Area of Coordinate Polygons

Geometry (NCTM)

Specify locations and describe spatial relationships using coordinate geometry and other representational systems.

Use coordinate geometry to represent and examine the properties of geometric shapes.

Use coordinate geometry to examine special geometric shapes, such as regular polygons or those with pairs of parallel or perpendicular sides.

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.

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.