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Find the area of the square in the figure.
Note:
1. A square lies inside a circle.
2. The square is shaded blue.
3. The circle is not shaded.
4. The equation given for the circle is x^2 + y^2 = 9.
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The problem is worded incorrectly and unprofessionally.
INCORRECTLY: it says " a square lies inside a circle ", which is insufficient
description to solve this problem.
A correct description is to say " a square is inscribed in the circle ".
UNPROFESSIONALLY: it requests to find the area of the square, but describes which part
is shaded and which is not. In this problem, it is EXCESSIVE and is NOT NECESSARY.
The shape, for which they request to find its area, is just defined above: it is the square inscribed in the circle.
Solution
From the given equation, the radius of the circle is = 3 units.
Hence, the diameter of the circle is two times the radius, i.e. 2*3 = 6 units.
Thus, the diagonal of the square is 6 units.
Let x be the side length of the circle. Then from Pythagoras
x^2 + x^2 = 6^2, i.e. 2x^2 = 36, x^2 = 36/2 = 18.
But x^2 is the square area.
At this point, we just completed the solution and got the
ANSWER. The area of the square is 18 square units.
Solved.