standard_description: Use special triangles to determine geometrically the values of sine, cosine, tangent for π/3, π/4 and π/6, and use the unit circle to express the values of sine, cosines, and tangent for π–x, π+x, and 2π–x in terms of their values for x, where x is any real number.
problem_activity: Task
Below are pictures of an equilateral triangle, a square, a regular hexagon, and a circle each having
the same perimeter:
[IMG]
Find the area of the equilateral triangle whose perimeter is $1$ unit.
Find the area of the square whose perimeter is $1$ unit.
Find the area of the regular hexagon whose perimeter is one unit.
Find the area of the circle whose perimeter is $1$ unit.
List the answers to (a), (b), (c) and (d) in increasing size.  How do you think the area of a regular octagon with perimeter $1$ unit would compare to the
triangle, square, hexagon, and circle?


aligns: no