### More estimates

Last time, I talked about the height of a hexagon; the strategy I used works with any shape with a pair of parallel sides. The parallel sides allow you to stack the polygons and add up the heights without having to worry about angles. For instance, it will work with a regular octagon. The picture to the left shows 5 stacked octagons that are slightly more than 12 square (otherwise in TileLand the top purple square would be wiped out). That means that 5 octagons > 12 squares or that 1 octagon > 12/5 =2.4 (since they are unit squares).

For those who like to exact lengths, you can break the height of an octagon up into three pieces. This diagram below demonstrates the breakdown: two half squares of length 1/ root 2 (since the diagonal is 1) and a rectangle with the long side of length 1. Root 2 plus 1 is 1.41421+1 = 2.41421.

Look forward to when I tackle odd sided polygons that don't have parallel sides.

For those who like to exact lengths, you can break the height of an octagon up into three pieces. This diagram below demonstrates the breakdown: two half squares of length 1/ root 2 (since the diagonal is 1) and a rectangle with the long side of length 1. Root 2 plus 1 is 1.41421+1 = 2.41421.

Look forward to when I tackle odd sided polygons that don't have parallel sides.