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

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giorgiana1976 | College Teacher | (Level 3) Valedictorian

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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)` .