## Poll

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**8 members have voted**

Here is the solution:

Start by graphing the equation x²+y²=10²

Then draw a line from equation x+y=5 & x+y=-5

The area in between both lines is the answer

5²+5²=10² × the length of both points of either line that contacts the circumference.

7.071 × 18.707 = 132.277

Does that answer look familiar? It does to me because that is the 1st & only answer I have ever given for this problem! Prove my work wrong 🙏

Quote:USpapergamesYou guys don't realize there is a difference between the average of all the different areas of a rectangle vs the average way a rectangle can be drawn. The rectangle only has 1/16 of the circumference of the circle to be drawn in, so 1/32 of the circle is your median answer since there is no mean randomly drawing inscribed rectangles. Tho I do like the idea of a mean of all potential areas but that is definitely a calculus problem. The hard part was calculating the length of the rectangle, not easy ;)

But your question was the average area of a random rectangle inscribed in a circle. So we need to know the distribution of all rectangles that can be so inscribed so the average of all those triangles can be taken.

Quote:unJonBut your question was the average area of a random rectangle inscribed in a circle. So we need to know the distribution of all rectangles that can be so inscribed so the average of all those triangles can be taken.

Think about the question a little harder. A rectangle can only be drawn so many different ways and the average of that must be halfway between all the sizes of the rectangle, not the area! It's obvious you guys aren't that good at word problems. The question says the average area of a rectangle, not all rectangles. Meaning this must be the average rectangle & then find it's area! No wonder nothing you guys were doing made any sense to me!

Shackleford's Question: What is the area of a rectangle randomly inscribed in a circle of radius 10?

Again, the rectangle is singular, not plural! Again, everyone is wrong except me, I win🏆. Equations don't lie just like computer simulations! But misinterpretation happens all the time in mathematics, I'm just surprised Shackleford could misinterpret the question even though he clearly posted the right wording of the question. This just goes to show you how easy it is to assume a question that you have solved previously many times. I really did think it had to be the wording of the question for everyone to misinterpret the answer :/

P.S. Try to use nothing but pen, paper & a basic calculator, your reliance on technology has stunted your equation skills. Bonus points for whoever gives me the equation & not just an explanation of how they got the correct answer ;)

Quote:USpapergamesLiterally, everyone is wrong except me because nobody spent any time trying to comprehend the question lol. They all thought it was a mean of all averages problem because they have seen so many similar calculus problems even though I'm shouting up & down that it's not a calculus problem & no trig required but everyone is just ignoring me as if I'm crazy instead of just asking for more information if nothing I was saying made any sense to you. After teaching high school math for 6 years I've learned the worst students are often the brightest but refuse to ask questions for fear of looking stupid.

Or maybe it's because nobody except you seems to have any idea what the definition of an "average rectangular prism" is. Average as defined in what way?