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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)
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)

This Question is Closed

madhu.mukherjee.946
 one year ago
Best ResponseYou've already chosen the best response.1find the area of the circle

madhu.mukherjee.946
 one year ago
Best ResponseYou've already chosen the best response.1what do you get?

madhu.mukherjee.946
 one year ago
Best ResponseYou've already chosen the best response.1so whats the area of the circle putting the radius

madhu.mukherjee.946
 one year ago
Best ResponseYou've already chosen the best response.1so whats the area for 3 circles

madhu.mukherjee.946
 one year ago
Best ResponseYou've already chosen the best response.1now find the area of the equilatral triangle as a whole,whats that

madhu.mukherjee.946
 one year ago
Best ResponseYou've already chosen the best response.1do you know the formula to find the area of equi triangle

madhu.mukherjee.946
 one year ago
Best ResponseYou've already chosen the best response.1@osanseviero

osanseviero
 one year ago
Best ResponseYou've already chosen the best response.1I'm working to get the formula, almost there

madhu.mukherjee.946
 one year ago
Best ResponseYou've already chosen the best response.1this is the formula

madhu.mukherjee.946
 one year ago
Best ResponseYou've already chosen the best response.1A=root3/4a^2

madhu.mukherjee.946
 one year ago
Best ResponseYou've already chosen the best response.1@osanseviero now you got it?

osanseviero
 one year ago
Best ResponseYou've already chosen the best response.1So sqrt(3)*l^2 / 4

madhu.mukherjee.946
 one year ago
Best ResponseYou've already chosen the best response.1dw:1441337140712:dw

madhu.mukherjee.946
 one year ago
Best ResponseYou've already chosen the best response.1this is the formula

madhu.mukherjee.946
 one year ago
Best ResponseYou've already chosen the best response.1now at the place of a^2 you will put l^2 as side of the triangle is l

osanseviero
 one year ago
Best ResponseYou've already chosen the best response.1So At = \[At = \frac{l ^{2} \sqrt{3} }{ 4 } 3\pi\]

beginnersmind
 one year ago
Best ResponseYou've already chosen the best response.1You 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
 one year ago
Best ResponseYou've already chosen the best response.1nice drawing:)

beginnersmind
 one year ago
Best ResponseYou've already chosen the best response.1Well, that's assuming that the 3 circles are tangent to each other and the sides of the triangle.

osanseviero
 one year ago
Best ResponseYou've already chosen the best response.1So how could I get a numeric answer?

osanseviero
 one year ago
Best ResponseYou've already chosen the best response.1Going to see this, thanks for the help https://www.youtube.com/watch?v=4lwhAfhRXXo

beginnersmind
 one year ago
Best ResponseYou've already chosen the best response.1There 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
 one year ago
Best ResponseYou've already chosen the best response.1The top region is P of course, not Q. Anyway, added a couple of hints about some angles and lines. dw:1441337851708:dw

beginnersmind
 one year ago
Best ResponseYou've already chosen the best response.1Anyway, the best idea would be to calculate l, then go from there.dw:1441338129100:dw This should be the simplest solution.

osanseviero
 one year ago
Best ResponseYou've already chosen the best response.1Ok. So I got that the side is l = 2r +2rsqrt(3). Since r is 1: l = 2 + 2sqrt(3)

beginnersmind
 one year ago
Best ResponseYou've already chosen the best response.1I got 2 + 4sqrt(3)

beginnersmind
 one year ago
Best ResponseYou've already chosen the best response.1sorry, that makes no sense. let me check

beginnersmind
 one year ago
Best ResponseYou've already chosen the best response.1dw:1441338549521:dw Yeah, 2+2sqrt(3) is correct.

beginnersmind
 one year ago
Best ResponseYou've already chosen the best response.1dw:1441338637803:dw

osanseviero
 one year ago
Best ResponseYou've already chosen the best response.1So the final area is around 3.5?

beginnersmind
 one year ago
Best ResponseYou've already chosen the best response.1Can you finish the rest? (hint use pythagoras to get the altitude and don't forget to subtract the area of the circles)

beginnersmind
 one year ago
Best ResponseYou've already chosen the best response.1let me check real quick

beginnersmind
 one year ago
Best ResponseYou've already chosen the best response.1Yeah, I got 3.504

beginnersmind
 one year ago
Best ResponseYou've already chosen the best response.1Cool. Sorry for leading you down the wrong path at first :)

osanseviero
 one year ago
Best ResponseYou've already chosen the best response.1No problem, thanks a lot for all the help
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