2005 AMC 10A Problems/Problem 20
Problem
An equiangular octagon has four sides of length 1 and four sides of length , arranged so that no two consecutive sides have the same length. What is the area of the octagon?
Solution
The area of the octagon can be divided up into 5 squares with side and 4 right triangles, which are half the area of each of the squares.
Therefore, the area of the octagon is equal to the area of squares.
The area of each square is , so the area of 7 squares is .