Mastering the Challenging Area of a Square: Two Easy Solutions ✨

Two solutions to this tricky area of a square are shared in this math video. The Geomtry used to solve the viral social media, "math for geniuses," or math olympiad style problem is high school level. That does not mean that finding the area of the square is simple.

To find the area of the square, one must apply properties of circles, discover parts of a right triangle, use the pythagorean theorem, then write systems of equations and use substitution to solve the system.

Another solution to finding the area of the square is shown that uses a pretty cool property of circles. If a chord is perpendicular to the diameter, the chord squares is equivalent to the product of the segments of the diameter created by the intersection of the chord and the diameter.

This approach means there is no need to create a right triangle and apply the Pythagorean Theorem to discover information used to find the area of the square in this tricky geometry problem.
The general case for the perpendicular chord-squared equivalence: https://youtu.be/VVxx7hjT2-c

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0:00 Intro
1:34 Method 1
5:04 Method 2