Consider an equilateral triangle and a square both inscribed in a unit circle such that one side of the square is parallel to one side of the triangle. Compute the area of the convex heptagon formed by the vertices of both the triangle and the square.
Solution
Consider the diagram above. We see that the shape is a square plus 3 triangles. The top and bottom triangles have base and height , and the triangle on the side has the same base and height . Adding their areas, we get the answer.
Want a route through all this instead of an archive? The track
puts 2,000 problems in a working order, from AMC 10 level to the IMO shortlist.