A square is inscribed in a circle such that each corner touches the circle.

Question

find a function that gives the area of the square as a function of the radius of the circle. Simplify the function as much as possible. and describe any symmetry in the function. Make certain to show all steps you use to come up with the function, as well as describe your reasoning. 

 

state the domain and range of the function you came up with in part a, keeping in mind all practical considerations.

Answer 1

Draw a diagram!

A diagonal of the square is a diameter of the circle.

diameter/diagonal = s√2, where s represents the side of the square

diameter/diagonal = 2r

2r = s√2

2r / √2 = s

r√2 = s

s² = area of square

(r√2)² = area of square

2r² = area of square

 

OR

 

The two diagonals of the square create four congruent right triangles.

The base and height of each is r

The area of each is r²/2

The area of all four is  2r²

 

Ain't math grand!