Grade 6 Math: Area of Polygons on the Coordinate Plane

Grade 6 focus: On the coordinate plane, you can find the area of polygons whose vertices are given as ordered pairs \((x,y)\). Common approaches: surround with a rectangle and subtract triangles, decompose into rectangles and right triangles, or use the shoelace formula when appropriate (often introduced later).

Video lesson: Watch this Anywhere Math lesson on polygons in the coordinate plane.

Rectangle method

1. Plot the vertices in order.
2. Draw a bounding rectangle whose sides align with the grid.
3. Subtract areas of right triangles or rectangles outside the polygon but inside the bounding box.

Decomposition method

Split the polygon into shapes with known area formulas (rectangles, right triangles). Add the areas.

Why coordinates help

Side lengths can be found from differences in \(x\) and \(y\) values when sides are horizontal or vertical.

Worked idea

For a rectangle with vertical/horizontal sides on the grid, width = difference in \(x\), height = difference in \(y\); area = width \(\times\) height.

Common mistakes

• Plotting points in the wrong order, crossing segments.
• Confusing \(x\) and \(y\) when finding side lengths.
• Using non-perpendicular “slanted” sides as if they were base/height without a proper height segment.

Practice tip

Use graph paper or a grid: sketch lightly, label every length you use in your calculations.