## AdhaZeera Group Title What area can the goat roam? one year ago one year ago

|dw:1350884315409:dw|

Fence SHED 4feet 5feet 8feet

3. UnkleRhaukus Group Title

|dw:1350884748553:dw|

4. UnkleRhaukus Group Title

ops i dident see the fence

5. Fellowroot Group Title

Can he go inside the shed? And is he/she connected by a chain that is connected to the corner of the shed?

6. UnkleRhaukus Group Title

|dw:1350884878590:dw|

No he's not connected. I'm not sure. That's all my teacher wrote

8. Fellowroot Group Title

he has to be connected by a chain to the shed right?

Wait... yes..

10. UnkleRhaukus Group Title

|dw:1350885122452:dw|

11. UnkleRhaukus Group Title

|dw:1350885496696:dw|

How do I calculate it?

13. UnkleRhaukus Group Title

break the shape in to smaller shapes

14. Fellowroot Group Title

Unkle Rhaukus I like your drawings, but what is the actual value?

81 sq ft??

16. Fellowroot Group Title

I'm very sure I know how to do it. Just give me some time to work it out.

17. Fellowroot Group Title

its not easy, but i'm still working.

18. Fellowroot Group Title

Ok, here it comes. Writing it up. :) !!!!!

You there?

20. Fellowroot Group Title

yeah hang on almost done

21. Fellowroot Group Title

you might be surprised but i got it.

22. Fellowroot Group Title

GOT IT!!!!

23. UnkleRhaukus Group Title

im not sure why you had to integrate

Thank you!

25. UnkleRhaukus Group Title

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

26. Fellowroot Group Title

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.

27. UnkleRhaukus Group Title

|dw:1350888457508:dw|

28. Fellowroot Group Title

@ 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.

29. UnkleRhaukus Group Title

|dw:1350888515709:dw|

30. UnkleRhaukus Group Title

the sector is 1/12 of a circle

31. Fellowroot Group Title

@ UnkleRhaukus I know that there is a formula that is A= (theta)r^2/2 but I don't how it works here.

32. UnkleRhaukus Group Title

$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$

33. UnkleRhaukus Group Title

well theta was 30° right? angles of segment / angle in circle $30°/360°=1/12$ area of segment / area of circle $\frac{\pi r^2}{12}\qquad/\qquad\pi r^2$

34. UnkleRhaukus Group Title

i had to use a trig ratio to to get 30° btw

35. Fellowroot Group Title

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.

36. UnkleRhaukus Group Title

where did i error?

37. Fellowroot Group Title

not sure, but its pretty darn good.

38. UnkleRhaukus Group Title

$A=\frac{\pi\times 3^2}4+\frac{\pi \times8^2}{2}+\frac{\pi \times8^2}{12}+\frac{4\times 8}{2}=\pi\times\frac{475}{12}+16\approx140.35$

39. UnkleRhaukus Group Title

@Fellowroot i think we got different answers because we were solving different regions our pictures are different

40. Fellowroot Group Title

|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.