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Geometry

# Composite Figures: Level 3 Challenges

The diagram consists of three nested squares. The lengths of the line segments are $$AB = 4, BC = 3,$$ and $$CD = 2$$.

What is the area of the smallest square?

What is the area of the large square?

$$ABCD$$ is a square of side length 1. Points $$E, F, G, H$$ are such that $$AE : EB = 1:1$$, $$BF: FC = 1 : 2$$, $$CG : GD = 1 : 3$$, $$DH : HA = 1 : 4$$.

What is the area of the quadrilateral $$EFGH$$?

A regular hexagon is inscribed in a circle, and 6 lines are drawn to join the vertices, resulting in the Aquarius Star, as shown above.

If the blue area is 120, what is the area of the yellow region?

Square BCDE has side length 12.
Area of triangle ACD is twice the area of square BCDE.
If AD intersects BE at F, what is the area of BCDF?

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