If the area of a square is 72 sq in find the radius?

Answer 1

The radius of a square is the radius of the circumcircle, ie the distance from the centre of the square to any vertex, which is half the length of the diagonal of the square.

Using Pythagoras:

diagonal^2 = side^2 + side^2

→ diagonal = √(2 x side^2)

area = side^2

→ diagonal = √(2 x area)

radius = 1/2 x diagonal = 1/2 x √(2 x area)

→ radius = 1/2 x √(2 x 72 sq in) = 1/2 x √(144 sq in) = 1/2 x 12 in = 6 in.

Answer 2

10