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# Area......

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1. Those words under the photo are Chinese characters(because I am from Hong Kong).

It means 'ABCD is a rectangle, the center of sector BE is A, the center of sector BF is C, find the area of the shaded region.(3 significant figures)'

2. 'Find the area of the figure shown above(3 significant figures)'

3. This question has English version. Great.

4. This too. Great.

5. This too. Great :D

Someone who knows pls comment below and don't forget to type the question number before the answer to identify which answer is to which question.

Jun 5, 2016
edited by MaxWong  Jun 5, 2016
edited by MaxWong  Jun 5, 2016
edited by MaxWong  Jun 5, 2016

#5
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2.

Picture the dots joined up to make a square of side 3cm.

The desired area is the area of this square + the area of 4*(3/4 of the area of a circle of radius 1cm) - 4*(the area of a semicircle of radius 1cm).

Area = (32 + 4*(3/4)*pi*12 - 4*(1/2*pi*12)cm2

Area = 9 + pi ≈ 12.142 cm2

Jun 5, 2016

#1
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1.

a. Area of the rectangle  - area of smaller sector  =  the "large" white area in the rectangle  =

[24 - 4pi] cm^2

b. Area of the large sector  - area of "large" white part of the rectangle = the total area of the shaded region =

[ 9pi - ( 24 - 4pi)] cm^2  = [ 13pi - 24] cm^2   = about 16.841 cm^2  = about 16.8 cm^2   Jun 5, 2016
#2
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Thx

MaxWong  Jun 5, 2016
#3
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3. Total area of sector  AOC =  pi(36)/ 3 =  12pi units^2

If the orange area = the blue area.....then, by symmetry......area BCEF   = the orange area

And the area of the sector formed by OED = the blue area.....so......all these areas are equal and they divide the total area of sector AOC into 4 equal parts.......so area ODEF  (1/2) the area of sector AOC  = 6pi units^2

So....we have that OD is the radius of the the smaller circle

And we have:

1/3 area of the smaller circle  =  Area ODEF  = [ pi * OD^2] / 3

6pi = [ pi * OD^2] / 3      multiply both sides by 3

18  = OD^2

OD  = √18 units   =  3√2 units  = about 4.24 units   Jun 5, 2016
#4
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5.

Area of sector OBC = pi (20)^2/ 6  = 200pi/3 cm^2

Area of equilateral triangle   (1/2) 20^2 sin60  = (1/2) 400* [√3/ 2] =  100√3 cm^2

Area between area of sector OBC and equilateral triangle = [ 200pi/3 -100√3] cm^2  →   (1)

And AC is the radius of the smaller circle  = (1/2)20cm  = 10cm

So....the shaded area = (1/2) area of the smaller circle  - (1)   =

[pi (10)^2/2  - (200pi/3 - 100√3) ] cm^2  = about 120.85 cm^2   Jun 5, 2016
#5
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2.

Picture the dots joined up to make a square of side 3cm.

The desired area is the area of this square + the area of 4*(3/4 of the area of a circle of radius 1cm) - 4*(the area of a semicircle of radius 1cm).

Area = (32 + 4*(3/4)*pi*12 - 4*(1/2*pi*12)cm2

Area = 9 + pi ≈ 12.142 cm2

Alan Jun 5, 2016
#8
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OK, Alan, thanks......I see that makes sense.....!!!   Jun 6, 2016
#9
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4. (Again).......!!!

The central angle formed  by two radial lines draw to each point of intersection of the two circles = 120°.......so.....the arc length, S, of the rest of one of the circles =   2pi(9)(240/360)  = 12pi

So......twice this = the length of the solid line in the figure = 24pi  = about 75.398 cm   Jun 6, 2016