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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.

Details:
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.

###### Image credit goes to Aniket Verma.
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