osanseviero
  • osanseviero
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
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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osanseviero
  • osanseviero
madhu.mukherjee.946
  • madhu.mukherjee.946
find the area of the circle
madhu.mukherjee.946
  • madhu.mukherjee.946
what do you get?

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More answers

osanseviero
  • osanseviero
pi*r^2
madhu.mukherjee.946
  • madhu.mukherjee.946
so whats the area of the circle putting the radius
osanseviero
  • osanseviero
pi
madhu.mukherjee.946
  • madhu.mukherjee.946
so whats the area for 3 circles
osanseviero
  • osanseviero
A = 3pi
madhu.mukherjee.946
  • madhu.mukherjee.946
now find the area of the equilatral triangle as a whole,whats that
madhu.mukherjee.946
  • madhu.mukherjee.946
do you know the formula to find the area of equi triangle
madhu.mukherjee.946
  • madhu.mukherjee.946
@osanseviero
osanseviero
  • osanseviero
I'm working to get the formula, almost there
madhu.mukherjee.946
  • madhu.mukherjee.946
this is the formula
madhu.mukherjee.946
  • madhu.mukherjee.946
A=root3/4a^2
madhu.mukherjee.946
  • madhu.mukherjee.946
@osanseviero now you got it?
osanseviero
  • osanseviero
So sqrt(3)*l^2 / 4
osanseviero
  • osanseviero
Just got it :)
madhu.mukherjee.946
  • madhu.mukherjee.946
|dw:1441337140712:dw|
madhu.mukherjee.946
  • madhu.mukherjee.946
this is the formula
madhu.mukherjee.946
  • madhu.mukherjee.946
now at the place of a^2 you will put l^2 as side of the triangle is l
osanseviero
  • osanseviero
So At = \[At = \frac{l ^{2} \sqrt{3} }{ 4 } -3\pi\]
madhu.mukherjee.946
  • madhu.mukherjee.946
exactly
beginnersmind
  • 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|
madhu.mukherjee.946
  • madhu.mukherjee.946
nice drawing:)
beginnersmind
  • beginnersmind
Well, that's assuming that the 3 circles are tangent to each other and the sides of the triangle.
osanseviero
  • osanseviero
They are
osanseviero
  • osanseviero
So how could I get a numeric answer?
osanseviero
  • osanseviero
Going to see this, thanks for the help https://www.youtube.com/watch?v=4lwhAfhRXXo
beginnersmind
  • 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)
beginnersmind
  • beginnersmind
The top region is P of course, not Q. Anyway, added a couple of hints about some angles and lines. |dw:1441337851708:dw|
beginnersmind
  • beginnersmind
Anyway, the best idea would be to calculate l, then go from there.|dw:1441338129100:dw| This should be the simplest solution.
osanseviero
  • osanseviero
Ok. So I got that the side is l = 2r +2rsqrt(3). Since r is 1: l = 2 + 2sqrt(3)
beginnersmind
  • beginnersmind
I got 2 + 4sqrt(3)
beginnersmind
  • beginnersmind
sorry, that makes no sense. let me check
beginnersmind
  • beginnersmind
|dw:1441338549521:dw| Yeah, 2+2sqrt(3) is correct.
beginnersmind
  • beginnersmind
|dw:1441338637803:dw|
osanseviero
  • osanseviero
So the final area is around 3.5?
beginnersmind
  • beginnersmind
Can you finish the rest? (hint use pythagoras to get the altitude and don't forget to subtract the area of the circles)
beginnersmind
  • beginnersmind
let me check real quick
beginnersmind
  • beginnersmind
Yeah, I got 3.504
osanseviero
  • osanseviero
Thanks!
beginnersmind
  • beginnersmind
Cool. Sorry for leading you down the wrong path at first :)
osanseviero
  • osanseviero
No problem, thanks a lot for all the help
beginnersmind
  • beginnersmind
No problem.

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