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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.