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Composite Figures

Overlap, inscribe, and circumscribe a collection of simple geometric shapes to make a complex, composite figure.

Composite Figures: Level 2 Challenges

         

In the regular star polygon above, \(\text{___________}.\)

The above shows a square inscribed in a circle, that is inscribed inside a larger square.

What fraction of the large square is shaded in red?

I have a square with side length 10.
I cut out 4 rectangles from each of its corners as shown above.
What is the perimeter of this new figure?

In the diagram above, a yellow regular hexagon lies inside a larger regular hexagon with twice as large a side length.

Each of the 3 line segments connecting the inner and outer hexagons has the same length as a side of the yellow hexagon.

Is it true that the 4 colored regions have the same area?

If each unit circle passes through the centers of the other 2 circles, what is the perimeter?

Do not include the parts that are contained within the figure.

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