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anonymous

  • one year ago

***WILL MEDAL AND FAN!!!*** A square with sides of https://suwannee.owschools.com/media/g_geo_2013/8/3rad2.gif is inscribed in a circle. What is the area of one of the sectors formed by the radii to the vertices of the square? a) 1.5pi b) 2.25pi c) 4.5pi

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  1. anonymous
    • one year ago
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    @phi

  2. anonymous
    • one year ago
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    |dw:1437403588550:dw|

  3. anonymous
    • one year ago
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    so i think thats what the question is saying, and you need to find the area of the coloured in section. s is the side of the square which is 3sqrt(2). r is the radius of the circle, which is also equal to half of the diagonal line of the square. so first, we have to figure out the diagonal line of the square. that can be done by using pythagorian equation: (side1)^2+(side2)^2 = diagonal length^2

  4. phi
    • one year ago
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    |dw:1437403532240:dw|

  5. anonymous
    • one year ago
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    Hence, (3sqrt(2))^2 + (3sqrt(2))^2 = d^2 Hence, d=6 (you can do the math following the equation above) so divide this by 2 in order to get the radius of the circle. therefore, r = 3 Next, you will notice that the coloured area we are looking for is only a quarter of the entire circle minus the area of a quarter of the entire square. So knowing that, first, you must the area of the circle using the equation: pi*r^2 = pi*(3)^2 = 9pi you need a quarter of that so divide it by 4 to get 9pi/4. Next, find the area of the square. length x width. So, 2*(3sqrt(2)) = 6sqrt(2) but similarly, you only need a quarter of that, so divide that by 4 to get 3sqrt(2)/2 Therefore, your final answer of the area of the coloured region will be the subtraction of the two areas: [(9pi/4)-(3sqrt(2)/2)] = (9pi-6sqrt(2))/4

  6. anonymous
    • one year ago
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    Is this considered to be a Trigonometry question?

  7. phi
    • one year ago
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    A sector is the shape of a piece of pie. The first step is to find the radius. The triangle is a 45-45-90 triangle, and you are given the hypotenuse

  8. anonymous
    • one year ago
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    which is 3 and the sqare root of 2

  9. phi
    • one year ago
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    the hypotenuse is \( 3 \sqrt{2} \) Do you remember (or have in your notes) how long is a side ? in a 45-45-90 triangle?

  10. anonymous
    • one year ago
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    Honestly no I don't. That's been almost a year ago since I was learning about that

  11. phi
    • one year ago
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    oh. math builds on itself and you end up using the old stuff... you can also use Kim's idea |dw:1437404053629:dw| and use the pythagorean theorem to find the diameter, and then find the radius

  12. phi
    • one year ago
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    pythagoras is very famous a^2 + b^2 = c^2 where a and b are the legs, and c is the hypotenuse

  13. anonymous
    • one year ago
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    I know I hear about the theorem every which way I turn! It's like the plague

  14. phi
    • one year ago
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    It is amazing how often it shows up. (but I would not call it a plague) Look on the bright side, if you know it, you know a *lot*

  15. anonymous
    • one year ago
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    Yeah

  16. phi
    • one year ago
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    can you find the diameter?

  17. anonymous
    • one year ago
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    Wouldn't that be the same as the hypotenuse?

  18. phi
    • one year ago
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    yes, of the last figure I posted.

  19. anonymous
    • one year ago
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    Sorry I left you hanging here. It was time to go

  20. phi
    • one year ago
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    did you finish this or is it too late?

  21. anonymous
    • one year ago
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    I didn't finish, but I really do need to though

  22. anonymous
    • one year ago
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    Can anybody help me?

  23. Loser66
    • one year ago
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    |dw:1437482709311:dw|

  24. anonymous
    • one year ago
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    Finally somebody to help. Thanks!

  25. Loser66
    • one year ago
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    hence the radius =3

  26. Loser66
    • one year ago
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    That gives us the area of the WHOLE circle is 9pi

  27. Loser66
    • one year ago
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    what you need? Because this guy is 1/4 of the circle |dw:1437482954457:dw|

  28. Loser66
    • one year ago
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    |dw:1437483048616:dw|

  29. phi
    • one year ago
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    fyi a sector is the two radius and the arc http://www.mathopenref.com/arcsector.html

  30. anonymous
    • one year ago
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    Let me look. I'll be right back. Thanks!

  31. anonymous
    • one year ago
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    @Loser66

  32. anonymous
    • one year ago
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    @AaronAndyson

  33. anonymous
    • one year ago
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    @dinosour1480

  34. anonymous
    • one year ago
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    @jamesr

  35. Nurali
    • one year ago
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    a² R² = ----- where a is the length of the side of the rectangle 2 In this case (3√2)² 9*2 R² = ------ = ----- = 9 2 2 so R = √9 => R = 3

  36. Nurali
    • one year ago
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    Now radii to the vertices form an angle of 90° so we have to find the area of a sector of angle 90° angle 90° area of sector = -------- * πR² = ------ * 3² * π 360° 360° area of sector =2.25π

  37. anonymous
    • one year ago
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    You made it sound so easy! Wow! Thanks!`

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