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What is pi? If the area of a circle is 49π, what is its circumference? If a circle is inscribed in a square, what is the ratio of the areas of the circle and the square?

In the above figure, which shaded area is larger?

The small circles all have the same size.

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Which of these shapes has an area that is different from the rest?

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When sketching out Leonardo Da Turtle, I started out with a green circle of radius 2, and then added a blue band across his eyes. The circular arcs of the blue band each subtend an angle of 60 degress at the center. And 2 triangles to fill in the gap. Finally, I added eyes of diameter 1.

What is the (visible) area of the blue band?

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Consider a triangle \(ABC\) with right angle \(A\), \(BC=5\) and \(AC=4.\) Three semicircles are drawn as in the figure above. Find the sum of the areas of the orange shaded regions.

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What is the perimeter of a semicircle with radius 7?

Use the approximation \( \pi \approx 22/7 \).

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