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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


A square and a "shuriken" (throwing star) are drawn over the \(4\times 4\) grid formed by 25 equally spaced dots, as shown above.

Which colored region has a larger area?

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.

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?

The figure above shows three consecutive squares of sides 5, 4 and 3, respectively.

Find the area of the black region.

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?


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