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## Composite Figures

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

# Composite Figures

If $$ACDE$$ is a rectangle and $$B$$ is a point on side $$AC$$ such that $$\triangle BED$$ is an equilateral triangle with side length $$36,$$ what is the area of the shaded region in the above diagram?

On each of the edges of an equilateral triangle with side length 28, we construct a semicircle with diameter 28 that extends outwards. The area of the enclosed figure has the form $$a \sqrt{b} + c \pi$$, where $$a, b,$$ and $$c$$ are integers and $$b$$ is not divisible by the square of a prime. What is the value of $$a+b+c$$?

If the side length of a regular octagon is $$8$$, what is the area of the octagon?

If the side length of a regular hexagon is $$6$$, what is the area of the hexagon?

What is the area of an annulus with inner radius $$3$$ and outer radius $$8?$$

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