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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

In the above diagram, $$ABCD$$ is a square and point $$E$$ lies on side $$CD$$.
Line segment $$AE$$ and diagonal $$BD$$ intersect at point $$F$$, such that $$BF : FD = 4 : 3$$.

If the combined area of the 2 blue triangles is $$100 \text{ cm}^{2}$$, find the area of the square in $$\text{cm}^{2}$$.


Note: The figure is not drawn to a scale

In a square, we draw a semicircle on the left side.
We also draw an isosceles triangle on the right side, with its apex at the center of the semicircle.

Which has a larger area, the yellow sector or the blue sector?

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.

A circle of radius 3 units is centered at $$(-1, -1)$$. Find the area of the region that lies inside the circle and inside the first quadrant (See figure).

The front face of Captain America's shield (refer to this image drawn to scale) is made up of 4 circles and a 5-pointed regular star polygon which are all concentric. The 5-pointed star is tangential to the smallest circle at the 5 points seen in the figure. The diameters of the 4 circles are 30, 23, 18 and 12 inches respectively (yes, those are the real dimensions). Calculate the ratio $$\frac{\mbox{blue and red coloured area}}{\mbox{white area}}$$.