## osanseviero one year ago Problem. You have an equilateral triangle (side l) with 3 circles inside of r=1. I need to calculate the area of the triangle (without the circle area)

1. osanseviero

find the area of the circle

what do you get?

4. osanseviero

pi*r^2

so whats the area of the circle putting the radius

6. osanseviero

pi

so whats the area for 3 circles

8. osanseviero

A = 3pi

now find the area of the equilatral triangle as a whole,whats that

do you know the formula to find the area of equi triangle

@osanseviero

12. osanseviero

I'm working to get the formula, almost there

this is the formula

A=root3/4a^2

@osanseviero now you got it?

16. osanseviero

So sqrt(3)*l^2 / 4

17. osanseviero

Just got it :)

|dw:1441337140712:dw|

this is the formula

now at the place of a^2 you will put l^2 as side of the triangle is l

21. osanseviero

So At = $At = \frac{l ^{2} \sqrt{3} }{ 4 } -3\pi$

exactly

23. beginnersmind

You can get an exact numeric answer. My terrible drawing shows how you can slice up the triangle into pieces that can be calculated exactly. |dw:1441336935522:dw|

nice drawing:)

25. beginnersmind

Well, that's assuming that the 3 circles are tangent to each other and the sides of the triangle.

26. osanseviero

They are

27. osanseviero

So how could I get a numeric answer?

28. osanseviero

Going to see this, thanks for the help https://www.youtube.com/watch?v=4lwhAfhRXXo

29. beginnersmind

There are three types of regions in my drawing, labelled P, Q and R. Can you find the area of either? (hint Q is a rectangle)

30. beginnersmind

The top region is P of course, not Q. Anyway, added a couple of hints about some angles and lines. |dw:1441337851708:dw|

31. beginnersmind

Anyway, the best idea would be to calculate l, then go from there.|dw:1441338129100:dw| This should be the simplest solution.

32. osanseviero

Ok. So I got that the side is l = 2r +2rsqrt(3). Since r is 1: l = 2 + 2sqrt(3)

33. beginnersmind

I got 2 + 4sqrt(3)

34. beginnersmind

sorry, that makes no sense. let me check

35. beginnersmind

|dw:1441338549521:dw| Yeah, 2+2sqrt(3) is correct.

36. beginnersmind

|dw:1441338637803:dw|

37. osanseviero

So the final area is around 3.5?

38. beginnersmind

Can you finish the rest? (hint use pythagoras to get the altitude and don't forget to subtract the area of the circles)

39. beginnersmind

let me check real quick

40. beginnersmind

Yeah, I got 3.504

41. osanseviero

Thanks!

42. beginnersmind

Cool. Sorry for leading you down the wrong path at first :)

43. osanseviero

No problem, thanks a lot for all the help

44. beginnersmind

No problem.