A square is inscribed in a circle of radius 7m. Find the area of the square.

To determine the area of the inscribed square, we need to
know the length of it's sides.

The diagonal of the square
is passing through the center of the circle and it represents the diameter of the
circle.

The diagonal of the square splits it in two right
angle isosceles triangles.

Since the diagonal represents
the hypotenuse and the legs of triangle are equal, then the other two angles of triangle
measure 45 degrees.

We'll use sine function to determine
the length of one leg of triangle.

sin 45 =
opp./hypotenuse

Let x be the length of the leg and the
hypotenuse is the diameter of the circle, which is 14
m.

`sqrt(2)` /2 =
x/14

`sqrt(2)` = x/7

x =
7`sqrt(2)`

Since we know the length of the side of the
square, we'll determine it's area:

A =
`x^(2)`

A = 7`sqrt(2)`
*7`sqrt(2)`

A = 98
`m^(2)`

The requested area of the square
measures 98 `m^(2)` .