How do you find the area of a figure using a grid?

Answer 1

You can't find the exact area of of most shapes with a grid, but you can get a pretty good approximation with the following method:

1) Count the number of squares completely inside the shape. Let's call this number X.

2) Count the number of squares that are partially inside the shape (squares with the shape's outline passing through them). We'll call this number Y.

3) A = X + 0.5Y

The answer is in squares, so you need to know the grid spacing if you want to convert to inches or something. Remember, this isn't exact. The smaller the squares, the better the results.

If you need to be really accurate, try the following:

4) Repeat steps 1 - 3 for a bunch of different grid sizes (e.g. 1", 0.5", 0.25". 0.125", etc.).

5) Graph the results from step 4 as Area vs. Grid Size.

6) Draw an approximate curve through the points you graphed, and estimate the asymptote as Grid Size approaches infinity. Carefully cut out the figure and mass it on a good balance. Cut out a square or rectangle of about the same size as the figure from the same grid paper and carefully mass it on the balance. You can then calculate the mass per grid square or mass per unit area. Divide the mass of the figure by mass per unit area and you have the area.