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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
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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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0dw:1437403588550:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so 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

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Hence, (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)] = (9pi6sqrt(2))/4

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Is this considered to be a Trigonometry question?

phi
 one year ago
Best ResponseYou've already chosen the best response.0A sector is the shape of a piece of pie. The first step is to find the radius. The triangle is a 454590 triangle, and you are given the hypotenuse

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0which is 3 and the sqare root of 2

phi
 one year ago
Best ResponseYou've already chosen the best response.0the hypotenuse is \( 3 \sqrt{2} \) Do you remember (or have in your notes) how long is a side ? in a 454590 triangle?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Honestly no I don't. That's been almost a year ago since I was learning about that

phi
 one year ago
Best ResponseYou've already chosen the best response.0oh. 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

phi
 one year ago
Best ResponseYou've already chosen the best response.0pythagoras is very famous a^2 + b^2 = c^2 where a and b are the legs, and c is the hypotenuse

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I know I hear about the theorem every which way I turn! It's like the plague

phi
 one year ago
Best ResponseYou've already chosen the best response.0It 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*

phi
 one year ago
Best ResponseYou've already chosen the best response.0can you find the diameter?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Wouldn't that be the same as the hypotenuse?

phi
 one year ago
Best ResponseYou've already chosen the best response.0yes, of the last figure I posted.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Sorry I left you hanging here. It was time to go

phi
 one year ago
Best ResponseYou've already chosen the best response.0did you finish this or is it too late?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I didn't finish, but I really do need to though

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Can anybody help me?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Finally somebody to help. Thanks!

Loser66
 one year ago
Best ResponseYou've already chosen the best response.0That gives us the area of the WHOLE circle is 9pi

Loser66
 one year ago
Best ResponseYou've already chosen the best response.0what you need? Because this guy is 1/4 of the circle dw:1437482954457:dw

phi
 one year ago
Best ResponseYou've already chosen the best response.0fyi a sector is the two radius and the arc http://www.mathopenref.com/arcsector.html

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Let me look. I'll be right back. Thanks!

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0a² 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

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Now 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

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0You made it sound so easy! Wow! Thanks!`
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