Senior Maths Challenge Help

the question is senior maths challenge 2022 Q20.
A square is inscribed inside a quadrant of a circle. The circle has
radius 10.
What is the area of the square?
A 25√
2 B 36 C 12π D 40 E 30√2

SO the correct answer is 40.

But the method i have done is getting me the area to be 100, and i do not know where i am going wrong.

What I have done is:

Firsty, i drew out a full circle, and divided it into four quadrants.
Then, in each quadrant, I have inscribed a square, as the question said.
So, now the diagram looks like a plus of 5 squares(the middle square comes from the each side of the surrounding 4 suares) inside a circle.
Then, i joined the very top right hand side of the corner of a square which is located in the quadrant, and joined it to the very bottom left corner of the square., so now i formed a diagonal. This diagonal is also known as the diameter of the circle as it touches the two pints of the circle and goes through the centre.
The diameter is 20 as the question said that the radius of the circle is 10.
So now, there will be a traingle with diagonal 20 and the shorter side x(which is the side of the square) and the longer side 3x(because this side is made up of each side of three squares.
Now, i would do pythagoras to find the side length of square :
(3x)^2+x^2=(20)^2
9x^2+x^2=400
10x^2=400
x^2=100
x=10

Therefore the area of the square is 100 as i have found out that the square is 10.

Unfortunately, this isnt the answer, and I dont know where I am going wrong, and I need help with this.

Thank you very much.

Reply 1

idkwhatXD_lol

OH NEVERMIND I MADE A MISTAKE IN THAT PYTHAGORAS PART 😆 10x^2=400 and then x^2 will be 40, not 100 😆 SILLY MISTAKES 😭

Reply 2

mqb2766

Original post by idkwhatXD_lol

OH NEVERMIND I MADE A MISTAKE IN THAT PYTHAGORAS PART 😆 10x^2=400 and then x^2 will be 40, not 100 😆 SILLY MISTAKES 😭

Without being funny, a sanity check would be the circle has area pi r^2 ~ 300 and a quadrant would be 75 ...

Reply 3

idkwhatXD_lol

Original post by mqb2766

Without being funny, a sanity check would be the circle has area pi r^2 ~ 300 and a quadrant would be 75 ...

OH YEA 😆 ty ill do that next time

Reply 4

mqb2766

Original post by idkwhatXD_lol

OH YEA 😆 ty ill do that next time

WIth a decent guestimate (so maybe half 75) sometimes you can rule out some answers and sometimes it gets you there. Probably more so for the earlier questions. You did the right approach by the sounds of it, and you noticed it wasnt one of the answers, so you knew something was up.

One way to check would be to work backwards, so if area is 100
10x^2 = 1000
so ... Similarly if the area is 40
10x^2 = 400
so sorted