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anonymous
 one year ago
Find the area of the shaded portion
https://flyingeaglesnv.sooschools.com/media/g_geo_2014/8/groupi60.gif
Answer box would only allow this as the answer:
A = x x (square root)x  xxPi
anonymous
 one year ago
Find the area of the shaded portion https://flyingeaglesnv.sooschools.com/media/g_geo_2014/8/groupi60.gif Answer box would only allow this as the answer: A = x x (square root)x  xxPi

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jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1dw:1437528564446:dw

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1if we cut the quadrilateral into 2 pieces, we get 2 congruent triangles dw:1437528642207:dw the 120 degree angle is also cut in half

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1this triangle is a 306090 triangle what is the value of x? dw:1437528698301:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0the x is the hypotenuse and that is 12. cuz the short leg (6) is 1/2 the size of the hypotenuse. right?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1x is the long leg actually. The hypotenuse is 2*6 = 12

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so then the long leg is 6(square root 3)

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1it turns out that x = 6*sqrt(3) template for a 306090 triangle dw:1437529004578:dw

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1dw:1437529045712:dw

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1What is the area of the triangle?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0area of the triangle is 1/2 (base x height) so it is 1/2 (6 square root (3)) (6) = 18 square root 3.

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1there are 2 of these triangles (one just mirrored over the hypotenuse to get the other) so the total area of this quadrilateral is 2*(18*sqrt(3)) = 36*sqrt(3)

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1dw:1437529313280:dw

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1to find the area of this shaded portion dw:1437529356277:dw use the formula A = (x/360)*pi*r^2 x = central angle r = radius leave the area in terms of pi

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so the area of the sector would be 12pi. So the area of the segment = area of sector  area of triangle. so A(segment) = 12pi  36(sqrt3) am I on the right track??

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1you subtracted in the wrong order the "12pi" area is smaller, so it needs to come second \[\large \text{area of shaded region} = \text{large area}  \text{small area}\] \[\large \text{area of shaded region} = \text{area of quadrilateral}  \text{area of sector}\] \[\large \text{area of shaded region} = 36\sqrt{3}  12\pi\]

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1and you should change "area of triangle" to "area of quadrilateral"

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Oh, so that is why i am coming up with a negative number. Thank you so much for your help. :)

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1you're welcome
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