Find the area of the regular polygon with the given radius or apothem. Leave your answer in simplest radical form.

Question

https://hudsonisd.instructure.com/assessment_questions/148995/files/439475/download?verifier=Vn4NJoR1vmmyQq934lNbCDzsPsgY2sP20F7EfpTk

Answer 1

Apothem: a = r cos (45) = (r√2)/2

Side length = base of blue triangle = r√2

Area of blue triangle: A_tr = 2r²/4

Area of square: A_sq = 4(A_tr) = 2r², where r = 6 cm is given

So A_sq = 2(6)² = 72 cm²