Please help.. I need to find the area of the shaded regions. could you please show me how you get the answer so i know how to

- anonymous

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- anonymous

##### 4 Attachments

- amistre64

the area of a sector as in #26 is given by the formula (radian angle) times r^2 divided by 2.
You have 2 different "radiuses" in #26 so we just take the larger area with radius (R) and subtract the inner/smaller area with radius (r) from it and your left with the shaded area.
What are the Radiusesses involved in #26?

- anonymous

8 and 2

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## More answers

- amistre64

Diameter is 8; radius is half of that = 4; inner radius is 4.
Add 2 to that to get 6 for the outer radius. Does this make sense so far?

- anonymous

ya

- amistre64

good; the shaded area is actually the area of half of a circle. if that makes sense;
radian measurement is pi.
Outer area - inner area = shaded area
6^2pi/2 - 4^2pi/2 = ShA
36pi/2 - 16pi/2 = ShA
18pi - 8pi = ShA
10pi is the area of the shaded region of #26.

- anonymous

so 10*pi?

- amistre64

yes; 10*pi should be the area of the shaded portion in #26

- anonymous

so 31.4

- amistre64

if we are going to use 3.14 to equal pi; then you are correct.

- anonymous

okay

- amistre64

#27 seems to be missing a measurement. the inner shading is 1 cm radius; and the total outer is 7 cm radius; but what would the radius be for the middle section?

- anonymous

it doesnt say

- amistre64

I cant see a way to figure it out with those measurements alone. maybe im missing something... lets try #28

- anonymous

ok

- amistre64

that is the area of the isoTriangle - the area of the inner circle, just gotta recall how to find area of the isoTriangle..

- amistre64

the triangle should have an area of:
21 + 7sqrt(3)/2 and we subtract 36pi from it to get the shaded area.

- amistre64

are there any "multiple choice" answers to choose from?

- anonymous

no

- anonymous

k

- amistre64

27.06217782 - 36pi does not seem correct....gonna have to try again :)

- anonymous

its 27.73883783

- amistre64

108sqrt(3) - 36pi...

- anonymous

ok

- amistre64

I get 73.96 as long as I did it right :)

- anonymous

ok

- amistre64

and I get:
36pi - 18pi - 18
18pi -18
18(pi -1)
18(2.14) = 38.52
thats the best I can do fer ya :)

- anonymous

for what one?

- amistre64

#29...but I gotta recalculate..
it should end up being:
18(pi - 2)
18(1.14) = 20.52
I lost track of one of my sectors :)

- amistre64

6*6 = 36; thats a square area;
pi(36)/4 = 9pi = 1 sector
pi(36)/4 = 9pi = another sector
both sectors together are 18pi.
36pi - 18pi - 36
18pi - 36
18(pi - 2)
18(1.14) = 20.52

- amistre64

thats all I can help you with; hope it helps :)

- anonymous

okay thank you

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