a regular rectangle is written in a cimcumferance of 8cm of the radius.a.)calculate the perimeter b.)calculate the longitude of the apothem

Question

And this is the last part to the question c.) calculate the area of the polygon. Well my math teacher is really strict on math so please answer this right. I didn't understand this entire question. I hope you can help me. Thank you!

Answer 1

a regular rectangle is a square

the radius is 8 cm

the radius is the hypotenuse of an isosceles right triangle; one leg is the apothem and the other is half of one side of the square

8²=a²+a²

64=2a²

32=a²

a=4√2 which is the answer to b.)

a.) the length of one side of the square is 2*4√2=8√2

     the perimeter is P=4s, P=4*(8√2)=32√2 cm

c.) A=s*s

     A=8√2*8√2

     A=64*2=128 square cm