1. What is the area of the shaded part of Figure 1? What is the area of the entire figure? What is the ratio of the whole area to the shaded area?

2. How many squares are there in Figure 2? What is the area of Figure 2 (the whole thing)? What is the area of one of the shaded triangles? What is the area of the shaded square (the square-within-a-square)? What is the ratio of the whole area to the shaded area?

3. In Figure 3, what is the area of the square-within-a-square (see Figure 2)? What is the area of the small shaded square in the corner? What is the ratio of the area of the square-within-a-square to the area of the small shaded square in the corner?

4. What fraction of the circle in Figure 4 is shaded? What is the ratio of the area of the entire circle to the area of the shaded part of the circle?

5. In Figure 5, what is the area of the shaded triangle? What is the area of the 10 cm x 10 cm square in the lower right corner? Is the area of the shaded part of the circle more or less than the area of the shaded triangle? Is the area of the shaded part of the circle more or less than the area of the square in the lower right corner?

6. In Figure 6, which is greater: the area of the 20 cm x 20 cm square, or the area of the circle that is drawn (inscribed) within the square? Which is greater: the area of the circle, or the area of the square-within-a square (see the shaded part of Figure 2)—which is inscribed within the circle? What is the ratio of the area of the 20 cm x 20 cm square to the area of the 10 cm x 10 cm square in the corner? What is the ratio of the area of the square-within-a square to the area of the 10 cm x 10 cm square in the corner? Do we know the exact ratio of the area of the circle to the area of the 10 cm x 10 cm square in the corner? Is it less than 4 to 1 (the ratio of the area of the 20 cm x 20 cm square to the area of the 10 cm x 10 cm square in the corner)? Is it greater than 2 to 1 (the ratio of the area of the square-within-a square to the area of the 10 cm x 10 cm square in the corner? What is the radius of the circle? What is the area of the radius squared? How does the area of the radius squared compare to the shaded area in Figure 1? Estimate: what is the ratio of the area of the circle to the area of the radius squared?

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