Find the Area of a Polygon Having Intersecting Sides

GeoMaster on the TI-84 Plus calculator can help you find the area of a polygon having intersecting sides. To find the area of a polygon having intersecting sides, break the polygon down into simple polygons (polygons whose sides intersect only at vertices) and then add up the areas of the simple polygons.

Sounds simple, but it’s not. To get GeoMaster to find the area of the smaller polygons, those polygons have to be constructed using the Polygon tool in the DRAW menu. But to construct a polygon using the Polygon tool, GeoMaster needs to know all the vertices of the polygon. So you must first find the point of intersection of the intersecting sides of the original polygon.

Again: Sounds simple, but it’s not. Unfortunately, GeoMaster’s Intersection tool can’t find the intersection of sides of polygons. So here’s what you can do to find the area of a polygon having intersecting sides:

  1. Press [GRAPH][WINDOW][3] to select the Segment tool from the DRAW menu. Construct segments over the sides of the intersecting sides of the polygon.

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  2. Press [GRAPH][WINDOW][ALPHA][PRGM] to select the Intersection tool from the DRAW menu and use this tool to find the point of intersection of the segments.

    If GeoMaster asks you which segment you want to select, choose the one with the highest number because this is the number of the most recently constructed segment. The second image shows the labeled point of intersection. You don’t have to do this, but you can if you want to.

  3. Press [GRAPH][WINDOW][6] to select the Polygon tool from the DRAW menu and use this tool to construct the smaller polygons contained in the polygon having intersecting sides.

  4. Press [GRAPH][ZOOM][2] to select the Area tool from the MEAS menu. Find the areas of the smaller polygons. Add these areas to find the area of the original polygon.

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