Square Flower
The diagram shows 8 circles surrounding a region. What is the perimeter of the shaded region?
Image
![Square Flower Square Flower](/sites/default/files/styles/large/public/thumbnails/content-id-10179-drawing.png?itok=yfD195Ye)
The shaded region is bounded by eight equal circles. The centres of the circles are at the corners and midpoints of the sides of a square.
The perimeter of the square is 8cm. What is the perimeter of the shaded region?
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The square has side length $2$cm, so each of the circles has radius $\frac{1}{2}$cm.
The circumference of a single circle, $2\pi r$, is therefore $\pi$cm.
The shaded region is bounded by $4$ halves of a circle and $4$ quarters of a circle.
Therefore the length of the perimeter of the shaded region is $$(4\times \frac{1}{2}+4\times\frac{1}{4})\pi=4\times \frac{3}{4}\times \pi= 3\pi cm.$$