Question

A square is inscribed in a circle of radius 3 square root 2 find the area

Answer 1

Inscribed means drawn inside with corners touching sides of circle

we know that r=3√2
if we double that we get the diameter of 6√2
this also is the diagonal of the square

we now have pythagoran theorem
the 2 legs are equal measure since it is a square
hypotonuse=diangoal of square

a^2+b^2=c^2
a=b
2a^2=c^2
2a^2=(6√2)^2
2a^2=72
divide both sides by 2
a^2=36
sqrt both sides
a=6
the legnth of one side is 6

area=side^2
area=6^2
area=36 

the area is 36 square units