Finding the area of a polygon

You already know area formulas for some basic shapes.

On this screen you will practice finding the area of polygons with as many as 12 sides! Start with the triangle in the figure. Use A= 1/2 b•h to find the area. Check your answer at the bottom of the screen.

Here's another method that works for lots of complicated polygons. The idea is to surround the polygon by a rectangle and then cut the part of the rectangle outside the polygon into simple pieces.

For example, in the figure, the area of the yellow triangle is the rectangle's area minus the area of two right triangles. Each of those triangles has base 13, height 8, and area 13 • 8/2 = 56.

Use the numbers on the vertical axis to see that the rectangle's top line has equation y = 19 and its bottom line is y = 3. So the height is 19 - 3, which is 16. Similarly, the width is 19 -5 = 14, and so the rectangle's area is 16•14 = 224. Subtract the two right triangle areas from the rectangle area to get the yellow triangle's area as 224 - 56 - 56 = 112.


Now comes the fun part. Drag the slider at the bottom back and forth to get polygons with more sides. Use the method described above to find the area of each of these polygons, starting with the quadrilateral (4 sides) and the pentagon (5 sides). In each case you need to cut away triangles from the polygon's surrounding rectangle. When you find the area of polygons with more than six sides, you may need to cut off trapezoids as well.

You can make your own polygons by dragging the black dots. However, all line segments joining two corners of the polygon must lie entirely inside it. Polygons with this property are called convex.