## stupidinmath one year ago ---

1. stupidinmath

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

2. ganeshie8

arc length : $$\large l = 2 (\theta)r \frac{\pi}{360}$$ now try

3. stupidinmath

oh, wrong formula. ok let me solve it:)

4. 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?

5. 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

6. ganeshie8

^^ Yes :)

7. stupidinmath

my arc length is 7.85 so.. my perimeter of the shaded region is 31.42 approximately. is that right?

8. ganeshie8

$$\large \color{red}{\checkmark}$$ next try if you get lncognlto's suggestion...

9. stupidinmath

ah, yes, thanks. and yup, what he said was right:) I just need a complete solution though:) thanks guys

10. ganeshie8

both methods are considered complete solutions :) u wlc :) however ur teacher wud get more impressed if u do the lncognlto's method...

11. stupidinmath

oh, haha, alright, will do that :)

12. ganeshie8

good :D

13. stupidinmath

@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)?

14. ganeshie8

Alright, here is the original formula :- arc length $$l = r\theta$$ $$\theta$$ is in radians

15. 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

16. ganeshie8

for the triangle, did they give u any dimensions ?

17. stupidinmath

thank you so much. yep, ill post my solution later for checking:)

18. lncognlto

May I give another thought? xD

19. stupidinmath

sure:)

20. ganeshie8

sure :)

21. 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.

22. stupidinmath

oh, that's right. smart one. Hahaha. will remember that:)

23. 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 !

24. stupidinmath

i believe so too:)