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mathsmarts
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a square is inscribed in a circle, each side of sq measures 4^2 in. Find an expression for the exact area of the shaded region... That being outside the square within the circle...I know how to get the shaded area.. I need the expression which is (16 pi  32) but I dont understand the answer. can you help with that???
 10 months ago
 10 months ago
mathsmarts Group Title
a square is inscribed in a circle, each side of sq measures 4^2 in. Find an expression for the exact area of the shaded region... That being outside the square within the circle...I know how to get the shaded area.. I need the expression which is (16 pi  32) but I dont understand the answer. can you help with that???
 10 months ago
 10 months ago

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Decart Group TitleBest ResponseYou've already chosen the best response.0
area of circle  area of square
 10 months ago

mathsmarts Group TitleBest ResponseYou've already chosen the best response.0
I know how to get the shaded area.. I need the expression which is (16 pi  32) but I dont understand the answer. can you help with that???
 10 months ago

DemolisionWolf Group TitleBest ResponseYou've already chosen the best response.0
is this correct? dw:1385249213040:dw
 10 months ago

mathsmarts Group TitleBest ResponseYou've already chosen the best response.0
dw:1385250369163:dw
 10 months ago

AllTehMaffs Group TitleBest ResponseYou've already chosen the best response.2
dw:1385250006166:dw The area of the shaded region of the problem you described is \[A= 128 \pi  256\]
 10 months ago

AllTehMaffs Group TitleBest ResponseYou've already chosen the best response.2
ah, in that case
 10 months ago

AllTehMaffs Group TitleBest ResponseYou've already chosen the best response.2
dw:1385250495005:dw
 10 months ago

AllTehMaffs Group TitleBest ResponseYou've already chosen the best response.2
on the right, it should say \[r=c/2\]
 10 months ago

jdoe0001 Group TitleBest ResponseYou've already chosen the best response.0
dw:1385251179646:dw
 10 months ago

mathsmarts Group TitleBest ResponseYou've already chosen the best response.0
YOU GUYS ARE AWESOME!!!
 10 months ago

mathsmarts Group TitleBest ResponseYou've already chosen the best response.0
how do I give you a metal?
 10 months ago

AllTehMaffs Group TitleBest ResponseYou've already chosen the best response.2
To understand the answer, we can look at another example. Say we have two rectangles, one that's 8x5 and another 2x5  the smaller one is inset in the other. dw:1385273283416:dw
 10 months ago

AllTehMaffs Group TitleBest ResponseYou've already chosen the best response.2
If we want to find the area of the "shaded region" (like in the circle problem) dw:1385273501118:dw we can subtract the area of the little rectangle from the bigger rectangle \[8*52*5 = 4010=30\] In this instance, it's easy to see that the shaded area is the larger area minus the smaller area  we check it knowing that the rectangular shaded region has dimensions 6x5 dw:1385273671303:dw \[6x5=30\] So the area of the shaded rectangle is proved to be equivalent to the area of the large rectangle minus the area of the small rectangle \[6*5 = 8*52*5\] \[30=4010\] \[30=30 \ \Huge \color{green} \checkmark\] Similarly, the answer in the back of the book gives the area of the larger circle dw:1385273946213:dw minus the area of the inscribed square dw:1385274015235:dw And the radius of the circle was found using the Pythagorean Thm. to find the diameter of the circle (and thus the radius) dw:1385274176101:dw
 10 months ago
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