Answer:
1)Area of circle: 64[tex]\pi[/tex]
2)Area of semicircles: 128[tex]\pi[/tex]
3)Area of quarter-circles: 128[tex]\pi[/tex]
4)Total area of pattern: 320[tex]\pi[/tex]
Step-by-step explanation:
r = 8cm
Given: 1 circle, 4 semicircles, and 8 quarter-circles.
Area of a circle: [tex]\pi r^{2}[/tex]
1) A = [tex]\pi r^{2}[/tex] where r = 8
A = 64[tex]\pi[/tex]
2) 4 semicircles = 2 circles
so the answer is 2*A = 128[tex]\pi[/tex]
3) 8 quarter-circles = 2 circles
Therefore, the answer here is the same as the answer for #2!
4)There are 5 circles total because:
1 circle = 1 circle
4 semicircles divided by 2 = 2 circles (because [tex]\frac{1}{2}[/tex] times 4)
8 quarter-circles divided by 4 (think about what "quarter" means) = 2 circles
So ... 1 + 2 + 2 = 5 circles
Now we need to find the area of 5 circles which is just 5*A
5*A = 320[tex]\pi[/tex]