options: Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.

Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.

Explain a proof of the Pythagorean Theorem and its converse.
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?


correct_option_index: 1