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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

         

All of the triangles in the diagram are equilateral and share a center with all the circles. All of the internal circles and triangles are inscribed in the appropriate triangles and circles, respectively.

If the green area is equal to the red area, is the purple area equal to the yellow area?

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.

\(ABCD\) is a square with points \(E\) and \(F\) lying on sides \(CD\) and \(AD,\) respectively. If the purple area is \([BHGI]=120,\) what is the sum of the pink areas \([AHF]+[FGED]+[ICE]?\)

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.

ABC is a right triangle as shown. Given that \(D\) is the midpoint of \(AB\), \(E\) is the midpoint of \(BC\), and the side lengths of \(AB\) and \(AC\) are both 12, find the area of the shaded region.

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