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jcherry99
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The diameter of the large circle = 3 diameters of the small circle.
The radius of the large circle = 3 radii of the small circles.

Step one
Find the radius of the large circle.
r_small = 5 cm             Given
r_large = 5 * 3 cm        Construction
r_large = 15 cm

Step Two
Find the Area of the large circle
Area = pi * r^2
Area = 3.14 * 15^2
Area = 3.14 * 225
Area = 706.5.

Step Three
Find the area of the 7 small circles.
r = 5 cm               given
pi = 3.14

Area = 3.14 * 5^2
Area = 3.14 * 25
Area = 78.5 cm^2

Area of 1 circle = 78.5 cm^2
Area of 7 circles = x                   Cross multiply
x * 1 = 78.5 cm^2 * 7
x = 549.5 cm^2

Step four
Find the area of the 6 congruent shapes (one of which is shaded). 

Area of the six congruent shapes = area of the large circle - area 7 small circles.

Area of seven large circle  =  706.5 cm^2
Area of 7 small circles        = 549.5 cm^2 Subtract
Area of 6 congruent shapes  157 cm^2

Step 5
Find the area of the shaded area 
6 congruent shapes = 157 cm^2           Cross multiply
1 shaded = x
 
6x = 1 * 157                                           Divide by 6
x = 157 / 6
x = 26.166667 cm^2  <<<<<<<<<<< answer

If your answer is in terms of pi then the answer us

X = 50 pi / 6 or 25 pi / 3   Alternate possibilities.

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