Geometry

# Composite Figures: Level 2 Challenges

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

5 unit circles are placed with their centers on a square grid. What is the total green area?

Note: The centers of the circles are $$(-1, 1), (1,1), (0,0), (-1,-1), (1,-1)$$.

The above shows a rectilinear figure (all its interior angles are either $$90^\circ$$ or $$270^\circ$$ only).

Calculate the perimeter of this figure.

Within the orange square, there are 4 circles each with radius 1. What is the area of the green region in the center?

Hint: Connect the centers of the circles.

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?

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