## mckenzieandjesus one year ago Find the area of the equilateral triangle. 4m square root ft2 12 squart root ft2 2 square root ft2 6mc053-4.jpg ft2

1. mckenzieandjesus

2. mckenzieandjesus

@jim_thompson5910

3. 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

4. jim_thompson5910

I'm guessing that point is the circumcenter and the length of 4 is the circumradius.

5. jim_thompson5910

|dw:1435281664406:dw|

6. mckenzieandjesus

ok

7. jim_thompson5910

draw in the other circumradii |dw:1435281712679:dw|

8. jim_thompson5910

each central angle is 360/3 = 120 degrees |dw:1435281776974:dw|

9. jim_thompson5910

and since we have an isosceles triangle |dw:1435281812412:dw|

10. 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)

11. anonymous

are you deriving the formula for the length of the side?

12. jim_thompson5910

break up the triangle into two pieces we will have a 30-60-90 triangle |dw:1435281907823:dw|

13. jim_thompson5910

I'm showing how to find the length of each side. Then we can use the formula $\Large A = \frac{\sqrt{3}}{4}s^2$

14. anonymous

oh i see

15. mckenzieandjesus

whats s?

16. jim_thompson5910

it's the length of each side of the equilateral triangle |dw:1435281897863:dw|

17. mckenzieandjesus

oh ok. so square root 3/4*4^2?

18. jim_thompson5910

s = 4 is false

19. mckenzieandjesus

ohh

20. jim_thompson5910

all of these drawings are building up to find s

21. Mertsj

|dw:1435281547572:dw|

22. jim_thompson5910

|dw:1435282026879:dw|

23. mckenzieandjesus

oh ok

24. jim_thompson5910

|dw:1435282090401:dw| what are x and y?

25. mckenzieandjesus

4?

26. jim_thompson5910

27. jim_thompson5910

notice how the short leg (opposite the 30 degree angle) is half of the hypotenuse

28. mckenzieandjesus

2 and 1?

29. jim_thompson5910

close |dw:1435282277842:dw|

30. jim_thompson5910

long leg = sqrt(3) times (short leg)

31. mckenzieandjesus

ohh

32. mckenzieandjesus

ohh i see

33. jim_thompson5910

the long leg is exactly half of s so that's why s = 2*(2*sqrt(3)) = 4*sqrt(3)

34. mckenzieandjesus

ah ok

35. jim_thompson5910

|dw:1435282367672:dw|

36. mckenzieandjesus

okay

37. mckenzieandjesus

So the answer is 4 square root 3 then. Not 12 square root 3

38. jim_thompson5910

$\Large s = 4\sqrt{3}$ |dw:1435282458289:dw|

39. jim_thompson5910

they want the area, NOT the side length

40. mckenzieandjesus

ohh oops

41. jim_thompson5910

plug that s value into the area formula $\Large A = \frac{\sqrt{3}}{4}s^2$

42. Mertsj

|dw:1435282443589:dw|

43. Mertsj

The triangle is divided into 3 congruent triangles.

44. Mertsj

Consider one of the triangles.

45. mckenzieandjesus

so $A = \frac{ \sqrt{3} }{ 4? } * S ^{2}$

46. mckenzieandjesus

oops ment to put 4 square root 3 for s

47. Mertsj

|dw:1435282544885:dw|

48. mckenzieandjesus

So would I put 4 square root 3 for s?

49. Mertsj

The area of that triangle is 1/2 base x height or $\frac{1}{2}\times 4\sqrt{3}\times 2=4\sqrt{3}$

50. Mertsj

Since there are three of those triangles, multiply that answer by 3

51. mckenzieandjesus

oh okay i added and got 12 square root 3

52. mckenzieandjesus

I guess it works either way lol thanku

53. Mertsj

54. Mertsj

Do you understand now?

55. mckenzieandjesus

Yes I do

56. mckenzieandjesus

Is the formula of a rectangle A=bh?

57. Mertsj

yes

58. mckenzieandjesus

or is it A= 1/2 bh?

59. Mertsj

A=bh

60. mckenzieandjesus

oh ok

61. mckenzieandjesus

thanku!