A square is inscribed in a circle of radius 12dm. what is the area of the square?
Radius bisects square, so use Pythagorean theorem.
x^2 + x^2 = 2x^2 = 12^2
Ok
To find the area of the square inscribed in a circle, we can use the following steps:
1. Draw the square inside the circle, with the four corners of the square touching the circle.
2. Since the square is inscribed in the circle, the diagonal of the square will be equal to the diameter of the circle.
3. The radius of the circle is given as 12dm. Therefore, the diameter of the circle is twice the radius, which is equal to 2 * 12dm = 24dm.
4. The diagonal of the square is equal to the diameter of the circle, which is 24dm.
5. In a square, the diagonal divides the square into two congruent right triangles.
6. Since the diagonal of the square is equal to 24dm, each leg of the right triangle (which is the hypotenuse of the right triangle) will be half of the diagonal, which is 24dm / 2 = 12dm.
7. The area of a square can be found by multiplying the length of one side by itself. So, the length of one side of the square is equal to the leg of the right triangle, which is 12dm.
8. Therefore, the area of the square can be calculated by squaring the length of one side. In this case, the area of the square is 12dm * 12dm = 144 square dm.
Therefore, the area of the square inscribed in the circle with a radius of 12dm is 144 square dm.