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)

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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)

Mathematics
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find the area of the circle
what do you get?

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Other answers:

pi*r^2
so whats the area of the circle putting the radius
pi
so whats the area for 3 circles
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
I'm working to get the formula, almost there
this is the formula
A=root3/4a^2
@osanseviero now you got it?
So sqrt(3)*l^2 / 4
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
So At = \[At = \frac{l ^{2} \sqrt{3} }{ 4 } -3\pi\]
exactly
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:)
Well, that's assuming that the 3 circles are tangent to each other and the sides of the triangle.
They are
So how could I get a numeric answer?
Going to see this, thanks for the help https://www.youtube.com/watch?v=4lwhAfhRXXo
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)
The top region is P of course, not Q. Anyway, added a couple of hints about some angles and lines. |dw:1441337851708:dw|
Anyway, the best idea would be to calculate l, then go from there.|dw:1441338129100:dw| This should be the simplest solution.
Ok. So I got that the side is l = 2r +2rsqrt(3). Since r is 1: l = 2 + 2sqrt(3)
I got 2 + 4sqrt(3)
sorry, that makes no sense. let me check
|dw:1441338549521:dw| Yeah, 2+2sqrt(3) is correct.
|dw:1441338637803:dw|
So the final area is around 3.5?
Can you finish the rest? (hint use pythagoras to get the altitude and don't forget to subtract the area of the circles)
let me check real quick
Yeah, I got 3.504
Thanks!
Cool. Sorry for leading you down the wrong path at first :)
No problem, thanks a lot for all the help
No problem.

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