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Geometry

# Composite Figures: Level 2 Challenges

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?

Three semicircles (with equal radii) are drawn inside the large semicircle so that their diameters all sit on the diameter of the large semicircle. What is the ratio of the red area to the blue area?

The above figure shows five congruent rectangles. A trapezoid is drawn in such a way that its vertices coincide with vertices of some of the rectangles. What percentage of the figure is shaded?

Rectangle $$DEFG$$ has square $$ABCD$$ removed leaving an area of $$92\text{ m}^2$$. Side $$AE = 4\text{ m}$$ and side $$CG = 8\text{ m}$$.

Determine the original area (in $$\text{m}^2$$) of rectangle $$DEFG$$.

Each circle in the diagram below has a radius of $$r = 6$$. What is the total area of the shaded regions?

By this construction, the distance from the center of one circle to its adjoining circles is equal.

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