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Composite Figures

Overlap, inscribe, and circumscribe a collection of simple geometric shapes to make a complex, composite figure. See more

Level 4


Let \(ABCD\) be a square and \(P\) be a point inside the square such that \(PB = 23\) and \(PD = 29\) . Find the area of \(\triangle APC\)

What is the minimum side length of a square which can contain 5 non-overlapping unit circles?

Give your answer to 3 decimal places.


Let \( ABCDE \) be a convex pentagon with \( \angle ABC= \angle BCD = 120^\circ \) and \([ABC]=[BCD]=[CDE]=[DEA]=[EAB]=12 \). Evaluate \([ABCDE] \) to 1 decimal place.

Notation: \( [ PQRS ] \) denotes the area of the figure \( PQRS \).
You may need to use a calculator to evaluate the area.

Two congruent squares \(ABCD\) and \(PQRS\) are positioned such that they share a common area defined by \(\Delta PQB\). The ratio of the area of \(\Delta PQB\) to the area of polygon \(AQRSPCD\) is \( \dfrac{3}{22} \).

If the side length of both squares is \(s\), then the perimeter of polygon \(AQRSPCD\) is \(\dfrac{m}{n}s\), where \(m\) and \(n\) are coprime positive integers. Find \(m+n\).

Find the area of \(\color{violet}{Violet}\) region (four square looking region of central circle) if radius of each circle is 4 units.

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Image credit goes to Aniket Verma.

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