mckenzieandjesus
  • mckenzieandjesus
Find the area of the equilateral triangle. 4m square root ft2 12 squart root ft2 2 square root ft2 6mc053-4.jpg ft2
Mathematics
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jamiebookeater
  • jamiebookeater
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mckenzieandjesus
  • mckenzieandjesus
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mckenzieandjesus
  • mckenzieandjesus
@jim_thompson5910
mckenzieandjesus
  • mckenzieandjesus
oops here Find the area of the equilateral triangle. 4 square root 3 ft2 12 square root 3 ft2 2 square root 3 ft2 6 square root 3 ft2

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jim_thompson5910
  • jim_thompson5910
I'm guessing that point is the circumcenter and the length of 4 is the circumradius.
jim_thompson5910
  • jim_thompson5910
|dw:1435281664406:dw|
mckenzieandjesus
  • mckenzieandjesus
ok
jim_thompson5910
  • jim_thompson5910
draw in the other circumradii |dw:1435281712679:dw|
jim_thompson5910
  • jim_thompson5910
each central angle is 360/3 = 120 degrees |dw:1435281776974:dw|
jim_thompson5910
  • jim_thompson5910
and since we have an isosceles triangle |dw:1435281812412:dw|
jim_thompson5910
  • jim_thompson5910
we know that these angles here |dw:1435281843370:dw| are 30 degrees each (solve x+x+120 = 180 for x to get x = 30)
anonymous
  • anonymous
are you deriving the formula for the length of the side?
jim_thompson5910
  • jim_thompson5910
break up the triangle into two pieces we will have a 30-60-90 triangle |dw:1435281907823:dw|
jim_thompson5910
  • jim_thompson5910
I'm showing how to find the length of each side. Then we can use the formula \[\Large A = \frac{\sqrt{3}}{4}s^2\]
anonymous
  • anonymous
oh i see
mckenzieandjesus
  • mckenzieandjesus
whats s?
jim_thompson5910
  • jim_thompson5910
it's the length of each side of the equilateral triangle |dw:1435281897863:dw|
mckenzieandjesus
  • mckenzieandjesus
oh ok. so square root 3/4*4^2?
jim_thompson5910
  • jim_thompson5910
s = 4 is false
mckenzieandjesus
  • mckenzieandjesus
ohh
jim_thompson5910
  • jim_thompson5910
all of these drawings are building up to find s
Mertsj
  • Mertsj
|dw:1435281547572:dw|
jim_thompson5910
  • jim_thompson5910
|dw:1435282026879:dw|
mckenzieandjesus
  • mckenzieandjesus
oh ok
jim_thompson5910
  • jim_thompson5910
|dw:1435282090401:dw| what are x and y?
mckenzieandjesus
  • mckenzieandjesus
4?
jim_thompson5910
  • jim_thompson5910
have a look at this page http://www.regentsprep.org/regents/math/algtrig/att2/ltri30.htm
jim_thompson5910
  • jim_thompson5910
notice how the short leg (opposite the 30 degree angle) is half of the hypotenuse
mckenzieandjesus
  • mckenzieandjesus
2 and 1?
jim_thompson5910
  • jim_thompson5910
close |dw:1435282277842:dw|
jim_thompson5910
  • jim_thompson5910
long leg = sqrt(3) times (short leg)
mckenzieandjesus
  • mckenzieandjesus
ohh
mckenzieandjesus
  • mckenzieandjesus
ohh i see
jim_thompson5910
  • jim_thompson5910
the long leg is exactly half of s so that's why s = 2*(2*sqrt(3)) = 4*sqrt(3)
mckenzieandjesus
  • mckenzieandjesus
ah ok
jim_thompson5910
  • jim_thompson5910
|dw:1435282367672:dw|
mckenzieandjesus
  • mckenzieandjesus
okay
mckenzieandjesus
  • mckenzieandjesus
So the answer is 4 square root 3 then. Not 12 square root 3
jim_thompson5910
  • jim_thompson5910
\[\Large s = 4\sqrt{3}\] |dw:1435282458289:dw|
jim_thompson5910
  • jim_thompson5910
they want the area, NOT the side length
mckenzieandjesus
  • mckenzieandjesus
ohh oops
jim_thompson5910
  • jim_thompson5910
plug that s value into the area formula \[\Large A = \frac{\sqrt{3}}{4}s^2\]
Mertsj
  • Mertsj
|dw:1435282443589:dw|
Mertsj
  • Mertsj
The triangle is divided into 3 congruent triangles.
Mertsj
  • Mertsj
Consider one of the triangles.
mckenzieandjesus
  • mckenzieandjesus
so \[A = \frac{ \sqrt{3} }{ 4? } * S ^{2}\]
mckenzieandjesus
  • mckenzieandjesus
oops ment to put 4 square root 3 for s
Mertsj
  • Mertsj
|dw:1435282544885:dw|
mckenzieandjesus
  • mckenzieandjesus
So would I put 4 square root 3 for s?
Mertsj
  • Mertsj
The area of that triangle is 1/2 base x height or \[\frac{1}{2}\times 4\sqrt{3}\times 2=4\sqrt{3}\]
Mertsj
  • Mertsj
Since there are three of those triangles, multiply that answer by 3
mckenzieandjesus
  • mckenzieandjesus
oh okay i added and got 12 square root 3
mckenzieandjesus
  • mckenzieandjesus
I guess it works either way lol thanku
Mertsj
  • Mertsj
And that is the answer.
Mertsj
  • Mertsj
Do you understand now?
mckenzieandjesus
  • mckenzieandjesus
Yes I do
mckenzieandjesus
  • mckenzieandjesus
Is the formula of a rectangle A=bh?
Mertsj
  • Mertsj
yes
mckenzieandjesus
  • mckenzieandjesus
or is it A= 1/2 bh?
Mertsj
  • Mertsj
A=bh
mckenzieandjesus
  • mckenzieandjesus
oh ok
mckenzieandjesus
  • mckenzieandjesus
thanku!

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