SOLUTION: Hello! Here is my question. I'm really having a hard time solving it and tried answering it many times. I don't know if how am I going to get it. Chord AB is 12√3 cm long and

Algebra ->  Customizable Word Problem Solvers  -> Geometry -> SOLUTION: Hello! Here is my question. I'm really having a hard time solving it and tried answering it many times. I don't know if how am I going to get it. Chord AB is 12√3 cm long and       Log On

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Question 1206037: Hello! Here is my question. I'm really having a hard time solving it and tried answering it many times. I don't know if how am I going to get it.
Chord AB is 12√3 cm long and the radius is 6 cm. Find the area of the shaded region.
Thank you to the tutor who can answer it! Thank you so much! =)
Cecile from Philippines
Found 5 solutions by math_tutor2020, greenestamps, Edwin McCravy, mccravyedwin, ikleyn:
Answer by math_tutor2020(3816) About Me  (Show Source):
You can put this solution on YOUR website!

Hi Cecile, welcome to the website. Unfortunately it seems your diagram isn't showing up. Please try your best to describe what the diagram looks like and what the shaded region looks like.

Perhaps a better alternative would be to upload your image on any online image hosting website (example: imgur) and then share the link for the tutors to have a look.

Edit: Tutor @greenestamps makes a great point I overlooked.
The diameter is the longest possible chord of a circle, so it's impossible to have 12%2Asqrt%283%29+=+matrix%281%2C2%2C20.7846%2C%22%28approximate%29%22%29 as a chord length when the radius is 6 and diameter is 12.

Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


The information you give is not possible.

If the radius is 6cm, then the diameter is 12cm. There can't be a chord of the circle that is longer than the diameter....

Fix the given information and re-post

Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!

I'm going to guess what your problem is.  I'll bet there are two concentric
circles, the smaller circle has a radius of OP = 6 cm. Chord AB is tangent to
the smaller circle at P. And AB = 12sqrt%283%29cm.  Find the area of the 
shaded region, the shaded segment of the larger circle.  Isn't that what
you want?



Draw the two radii OA and OB of the larger circle (in red):



PA=expr%281%2F2%29AB=expr%281%2F2%29%2A12sqrt%283%29=6sqrt%283%29

Use the Pythagorean theorem on right triangle OPA.
OA%5E2=OP%5E2%2BPA%5E2
OA%5E2=6%5E2%2B%286sqrt%283%29%29%5E2
OA%5E2=36%2B36%2A3
OA%5E2=36%2B108
OA%5E2=144
OA=sqrt%28144%29
OA=12 = radius of larger circle.

Triangle OPA is a 30-60-90 right triangle because its shortest side OP=6 cm
and its longest side OA, is 12, twice the shortest side.

So angle AOP = 60o = π/3 radians, and angle AOB = 120o = 2π/3 radians.
We find the area of the sector OAB and subtract the area of triangle OAB.

Area of the sector is 

Area of triangle AOP = expr%281%2F2%29%2AAP%2APB=expr%281%2F2%29%2A6%2A6%2Asqrt%283%29=18sqrt%283%29

Area of triangle AOB = twice area of AOP = 36sqrt%283%29

Subtract the area of the triangle from the area of the sector:

48pi-36sqrt%283%29%22%22=%22%2212%284pi-3sqrt%283%29%29

About 88.4 cm2.

Edwin

Answer by mccravyedwin(406) About Me  (Show Source):
You can put this solution on YOUR website!

I corrected the errors I had on the solution above, so I thought
I'd better let you know in case you got the solution before I
corrected it.

Edwin

Answer by ikleyn(52767) About Me  (Show Source):
You can put this solution on YOUR website!
.

Cecile, it is a bad style to post incomplete problems.

It is the same as to walk in a street with one sock.

It is the same as to walk in a street with one sock, saying that you have a hard time wearing the second sock.