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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 3 Challenges

         

The side of the square is \( a \). Express the green area with \( a \).

Each square's vertex is a circumcentre of appropriate circular arc.

All the green triangles above are equilateral triangles.

What is the area of the triangle labelled as \(A\) \(\big(\)in \(\text{cm}^2\big)?\)

7 non-overlapping unit circles are inscribed inside a large circle as shown below. What is the area of the shaded region?

Round your answer to 3 decimal places.

What is the area of the region enclosed by the graph of \(x^2+y^2=|x|+|y|\)?

\[\] Notation: \( | \cdot | \) denotes the absolute value function.

A rectangle is divided by four lines, as shown, with 4 of the resulting triangles having known areas. Find the area of the quadrilateral that is shaded in pink.

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