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What area can the goat roam?

Mathematics
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|dw:1350884315409:dw|
Fence SHED 4feet 5feet 8feet
|dw:1350884748553:dw|

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Other answers:

ops i dident see the fence
Can he go inside the shed? And is he/she connected by a chain that is connected to the corner of the shed?
|dw:1350884878590:dw|
No he's not connected. I'm not sure. That's all my teacher wrote
he has to be connected by a chain to the shed right?
Wait... yes..
|dw:1350885122452:dw|
|dw:1350885496696:dw|
How do I calculate it?
break the shape in to smaller shapes
Unkle Rhaukus I like your drawings, but what is the actual value?
81 sq ft??
I'm very sure I know how to do it. Just give me some time to work it out.
its not easy, but i'm still working.
Ok, here it comes. Writing it up. :) !!!!!
You there?
yeah hang on almost done
you might be surprised but i got it.
im not sure why you had to integrate
Thank you!
we know the are of a circle is πr^2, so a semicircle has area (πr^2)/2 and a quater circle has area (πr^2)/4
I integrated because I wanted to take the whole circle and then subtract the parts where the goat can't go. The area of the top of the circle is curved and the goat can't go there. So I created a function and integrated it so that I could find that exact area that is fenced off.
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@ AdhaZeera Do you understand what I did when I integrated. I will explain it to you if you want. I used calculus to arrive at that answer.
|dw:1350888515709:dw|
the sector is 1/12 of a circle
@ UnkleRhaukus I know that there is a formula that is A= (theta)r^2/2 but I don't how it works here.
\[A=\frac{\pi\times 3^2}4+\frac{\pi \times8^2}{2}+\frac{\pi \times8^2}{12}+\frac{4\times 8}{2}\]\[=\pi\times\frac{465}{12}+16\]\[\approx 140\]
well theta was 30° right? angles of segment / angle in circle \[30°/360°=1/12\] area of segment / area of circle \[\frac{\pi r^2}{12}\qquad/\qquad\pi r^2\]
i had to use a trig ratio to to get 30° btw
Your value comes to 140.35 mine is 141.7, its off only by a hair and is a very good approximation, but mine is exact.
where did i error?
not sure, but its pretty darn good.
\[A=\frac{\pi\times 3^2}4+\frac{\pi \times8^2}{2}+\frac{\pi \times8^2}{12}+\frac{4\times 8}{2}=\pi\times\frac{475}{12}+16\approx140.35\]
@Fellowroot i think we got different answers because we were solving different regions our pictures are different
|dw:1350891993500:dw| The only thing I don't know if that if the 5 feet fence touches the edge of the circle or if there is a gab. For the solution i provided it doesn't matter though. On my pic, the 'x', I really don't know that distance, it may make a difference for your answer, i don't know.

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