Given that the area of a square inscribed in a circle is 64 cm^2, how do you find the area of the circle?

1 Answer
Jun 9, 2015

Answer:

area of the circle # =color(purple)( 100.48 cm^2#

Explanation:

Area of the square # = 64cm^2#
So the side of this square # =color(purple)( sqrt64 = 8cm#
And the diagonal of this square # = sidesqrt2 =color(purple)( 8sqrt2#

Given that the square is inscribed inside the circle , the diagonal of this square #=# the diameter #(d)# of the circle.

# color(purple)(8sqrt2) = d#
So, the radius , #color(purple)(r = 4sqrt2#

Now , the area of the circle # = pi(r)^2#
# = 3.14 xx color(purple)((4sqrt2)^2#
# = 3.14 xx color(purple)(16 xx 2#

# =color(purple)( 100.48 cm^2#