Question 328364: A square is inscribed in a circle of radius 12mm. What’s the area of the square?
Answer by jessica43(140)   (Show Source):
You can put this solution on YOUR website! First draw the picture of the square inscribed inside a circle. Next draw in one diagonal of the square so the square is cut into 2 right triangles. Looking at the picture, you should be able to see that this diagonal of the square is the same as the diameter of the circle. Since we know the radius of the circle is 12mm, then the measure of the diameter is 24mm (2r=d).
Now we need to use the pythagorean theorem (a^2 + b^2 = c^2) to find the length and the width of the square. We can use this because we divided the square into right triangles and we know the length of the hypotenuse (the diagonal of the square or diameter of the circle).
So we have:
a^2 + b^2 = c^2
a^2 + b^2 = 24^2
Since this is a square, we know that sides a and b must be of equal length, so a=b. We can then change the b in the equation to an a:
a^2 + a^2 = 24^2
2a^2 = 24^2
2a^2 = 576
a^2 = 288
a = sqrt(288) = 16.971
So the length of each side of the triangle are 16.971mm.
Now looking again at your picture, you will see that the sides of the triangle are the same as the length and width of the square. So now we use the area of a square formula:
A = L*W
A = 16.971*16.971
A = 288
So the area of the square is 288mm squared.
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