anonymous
  • anonymous
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Mathematics
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
I'm quite confused. i dont know now T.T arc length: l = 2(theta)(r)(theta/360) l = 2(90)(5)(90/360) l=225 225x4 = 900 perimeter is 900cm
ganeshie8
  • ganeshie8
arc length : \(\large l = 2 (\theta)r \frac{\pi}{360}\) now try
anonymous
  • anonymous
oh, wrong formula. ok let me solve it:)

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lncognlto
  • lncognlto
This is just a thought, but wouldn't the perimeter of the shaded region be equal to the circumference of a circle with a radius of 5 cm?
ganeshie8
  • ganeshie8
Or, you can see that there are four quarter arcs of radius 5 which give u 1 complete perimeter of circle of radius 5
ganeshie8
  • ganeshie8
^^ Yes :)
anonymous
  • anonymous
my arc length is 7.85 so.. my perimeter of the shaded region is 31.42 approximately. is that right?
ganeshie8
  • ganeshie8
\(\large \color{red}{\checkmark}\) next try if you get lncognlto's suggestion...
anonymous
  • anonymous
ah, yes, thanks. and yup, what he said was right:) I just need a complete solution though:) thanks guys
ganeshie8
  • ganeshie8
both methods are considered complete solutions :) u wlc :) however ur teacher wud get more impressed if u do the lncognlto's method...
anonymous
  • anonymous
oh, haha, alright, will do that :)
ganeshie8
  • ganeshie8
good :D
anonymous
  • anonymous
@ganeshie8 , if this is the problem.. would the formula still be 2(theta)(r)(pi/360) or it should be 2(theta)(2)(pi/180)?
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ganeshie8
  • ganeshie8
Alright, here is the original formula :- arc length \(l = r\theta\) \(\theta\) is in radians
ganeshie8
  • ganeshie8
to convert given \(\theta\) degrees into \(\theta\) radians, u multiply \(\frac{2\pi}{360}\) which is same as multiplying \(\frac{\pi}{180}\) :- arc length \(l = r \theta \frac{2\pi}{360}\) \(\theta\) is in degrees now
ganeshie8
  • ganeshie8
for the triangle, did they give u any dimensions ?
anonymous
  • anonymous
thank you so much. yep, ill post my solution later for checking:)
lncognlto
  • lncognlto
May I give another thought? xD
anonymous
  • anonymous
sure:)
ganeshie8
  • ganeshie8
sure :)
lncognlto
  • lncognlto
If this triangle is equilateral, then the angles of each of the sectors is going to be 60 degrees. Thus three sectors together make 180 degrees, or half a circle. So the perimeter of the shaded region would then be equal to half the circumference of a circle with the radius equaling half the length of a side of the triangle.
anonymous
  • anonymous
oh, that's right. smart one. Hahaha. will remember that:)
ganeshie8
  • ganeshie8
60 + 60 + 60 and 180 which one save u time ha ? I'm sure ur teacher wants u do this exactly as lcognlto suggests !
anonymous
  • anonymous
i believe so too:)

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