Answer:
Step-by-step explanation:
(1) As definition, the area () of a circle is calculated by:
x
with
is radius of circle.
(2) The relation between radius () and diameter (
) of a circle is:
= 2 x
(3) Applying the Pythagorean theorem for a square with sides of length ,
the relation between side and diagonal
is:
=> The diagonal () of that square is calculated by:
=
(4) The square fits exactly inside a circle, with each of its vertices being on the circumference of the circle.
Applying the theorem of inscribed angle in a circle, the measure of arc BD is twice as the measure of inscribed angle BAD.
In other words, the measure of arc AC = 2 x 90 = 180 deg, or half of circle.
It means that the diagonal BD is coincide with a diameter of circle.
=>
or x
=
or =
Substitute back into original formula used for calculating the area of circle:
=> A = x
=
x
=> x
=> x
=
x
= 5.97 cm
Hope this helps!
:)