Help with finding the area of the enclosed, curved quadrilateral.

- Rizags

Help with finding the area of the enclosed, curved quadrilateral.

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- Rizags

##### 1 Attachment

- Rizags

Not a quadrilateral, just a curved four sided thing in the middle

- ybarrap

|dw:1449527843071:dw|

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- Rizags

yes. The actual goal is to find the overlapping areas where the circle portions overlap each other, but if i get the center area, I think i can calculate the rest.

- ybarrap

Ok, so you want these areas?
|dw:1449528016942:dw|

- Rizags

yes, preferably but whichever area is easier was my initial goal.

- Rizags

In other words, with the area of the center piece, i can get the areas of those overlaps

- ybarrap

brb, let me try a few things

- Rizags

ok thanks

- ybarrap

|dw:1449528799608:dw|

- ybarrap

brb

- Rizags

i'm really sorry, shoulda clarified, it's a circle with one-fourth of its radius in the square. I didn't think that was relevant

- Rizags

but if i can treat it as an ellipse and get the same answer that should be fine actually

- ybarrap

Subtract out area of triangle from area of sector to get the area of circular section inside:
|dw:1449530698995:dw|

- Rizags

and then if i multiply that area by 4, I get an overcount

- ybarrap

Check this out...

- ybarrap

|dw:1449533727558:dw|

- Rizags

that would give the area of the outside portions whilst counting the overlap only once i think

- ybarrap

Seems like there is an inconsistency with the problem. In order to have a side equal to 2 and a circle of radius 2, then the distance \(x\) needs to be 1.322 not 1:
|dw:1449535226592:dw|
|dw:1449535462949:dw|

- Rizags

would it be correct if 0.5 was one fourth of the diamter instead?

- ybarrap

Still inconsistent:
|dw:1449535868469:dw|

- ybarrap

Are the sides really 2?

- Rizags

My prof is honestly a little weird. here's what i have accumulated thus far:|dw:1449536068242:dw|

- ybarrap

So the side is sqrt(3) not 2?

- Rizags

Also |dw:1449536161493:dw|

- Rizags

well, the side has to be sqrt(3) times the radius of the circle, it must be. I'm going to disregard his silly measurements

- ybarrap

Yes, that is the length of the chord you've drawn, but that's the problem you setup

- Rizags

if i let r=2 for his purposes, i'm still faced with the same issue

- ybarrap

That IS the area of the triangle, though

- ybarrap

I'm confused about what the problem is now

- Rizags

Same exact picture, I need to find the area of the little overlaps

- Rizags

I have the area of the sector portions ALONE, but i need another piece of information

- ybarrap

ok

- ybarrap

makes more sense now

- ybarrap

|dw:1449537473730:dw|