Find the area of the equilateral triangle. 4m square root ft2 12 squart root ft2 2 square root ft2 6mc053-4.jpg ft2

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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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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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Other answers:

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

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