Question

I can't figure out how to find the area of the shaded region in this circle, for some reason its just not making sense to me.

Answer 1

You're not done drawing the figure. I can show you on twiddla

Answer 2

http://www.twiddla.com/solved

Answer 3

so it makes sense to me that the length of each arc is 1/4 of the circumference, so at least
half of the area of the circle is contained in shaded area.

Answer 4

i just don't know how to proceed further if if don't know the radius
of the circle

Answer 5

Yeah, I was just going to say that we don't know the radius of the circle yet

Answer 6

Why are the 90 degree quadrants marked?

Answer 7

i think so you know that the length of each arc is a 1/4 of the circumference of the whole circle

Answer 8

Nothing to do with the shaded figure?

Answer 9

i don't think so

Answer 10

OK, so they are nothing to do with anything then, just checking...

Answer 11

If that's all they gave u, have to assume radius r and give the answer in terms of r (assuming it is possible, I haven't really looked at it yet)

Answer 12

They haven't even specified that O is centre, assume it is....

Answer 13

So what do u think, r u expected to provide "algebra" responses or is that not something u wre expecting?

Answer 14

the answer is supposed to be an actual number

Answer 15

i know the area of each unshaded region is (1/2)(2 ft)(length of the chord)

Answer 16

i think the right triangles you could draw would be 45-45-90 triangles

Answer 17

I can give it algebraically because there is a formula for the segment but needs either length of segment or angle at centre or radius, none of which we have or can get.

Drawing triangles won't help because u only have one length and cannot get more.

I will think about it a little more, I am fairly sure a numerical answer is not possible.

Answer 18

I'm starting to be convinced that the radius is 2sqrt{2}

Answer 19

The angles are 45 degree angles.
Thus radius = 2sqrt(2)
Area of 90 degree sector = 2*pi
Area of triangle = 4
Total shaded area = 4+4+2pi+2pi = 8+4pi

Answer 20

cool. that is what i was starting to think.

Answer 21

Welp, looks like dumbcow got it

Answer 22

The angles are 45 degree angles.

How do u get this?

Answer 23

OK u take bisection at centre, fair enough.

Answer 24

If theta is angle of one triangle, then 90-thets is angle of other triangle
cos(theta) = 2/r
cos(90-theta) = sin(theta) = 2/r
cos = sin --> theta = 45

Answer 25

So, which triangles?

Answer 26

If theta is angle of one triangle, then 90-thets is angle of other triangle cos(theta) = 2/r cos(90-theta) = sin(theta) = 2/r cos = sin --> theta = 45

This is just a circular argument...

Answer 27

drawing a line from the center point to each end of the chord

Answer 28

Look at my pic...

Answer 29

U see 45 degrees there?

Answer 30

i'm not sure, honestly it took me forever to figure out what to do looking at my original picture

Answer 31

i haven't done geometry for five years

Answer 32

The only way it could possibly work out (I think) is id¡f thye corners of the shaded area were aligned with the 90 degree points that are marked.

Otherwise there are many different circles that could match the 2 feet dimension.

Answer 33

i agree. the only reason i came to the conclusion i did is because of the 90 degree markers

Answer 34

But in the picture they are not aligned...

Answer 35

And I think u cannot assume it....( or u can assume it and say u have)

Answer 36

Well, let me know if u think I have it wrong....