Question 947896: Diameter of a circle is 4cm. There is a square inside the circle with all four corners touching the circle. I am asked what is the area of the square.
Simplest way to calculate mentally.
Answer by Zucchini(70)   (Show Source):
You can put this solution on YOUR website! The first thing you need to realize is that when you draw in the diameter, it will cut the square into two triangle. The diameter is 4cm., so the hypotenuse of the triangle will be 4cm. The other two sides are congruent because the the sides of the square are congruent. (It's easier if you draw a picture and look at it rather than picture it in your mind). So we know that the triangles are 45-45-90 triangles because two of sides are congruent and all the angles of a square are 90 degrees. So, the two other sides are 4/|2 (the "|" stands for the square root). That simplifies to 2 times the square root of 2. So, now you multiply 2 times the square root of two by 2 times the square root of two. That simplifies to four times the square root of four, which can then be further simplified to four times two, which is 8. So, the area of the square is 8 sq cm.
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