Thread: GRE Math problem help!

I'm trying to figure out an easy way to solve this problem:

The figure above shows the lengths of the sides of an equiangular polygon. What is the area of the polygon? (My note: Since I can't draw the figure, I'll explain it. The figure has 8 sides with lengths 1 and sq. rt. 2 alternating on each side.)

The answer is 7, but I can't seem to get to this answer. Any help?

Originally Posted by Azure8011

I'm trying to figure out an easy way to solve this problem:

The figure above shows the lengths of the sides of an equiangular polygon. What is the area of the polygon? (My note: Since I can't draw the figure, I'll explain it. The figure has 8 sides with lengths 1 and sq. rt. 2 alternating on each side.)

The answer is 7, but I can't seem to get to this answer. Any help?

enclose the octagon with a square ... Area = (big square) - (4 corner triangles) = (big square) - (2 small squares w/ diagonal length 1) = $\displaystyle (2\sqrt{2})^2 - 1 = 7$