Area of Coordinate Polygons

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.

Steps to Find the Area of a Coordinate Polygon:

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

Example:

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.

Study Guide:

• 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!