Composite Figures: Level 3 Challenges Practice Problems Online

The 2 green points in the diagram are the midpoints of 2 adjacent sides of a regular hexagon.

Which is larger, the red area or the blue area?

The diagram above shows that a semicircle is inscribed in a quartercirclewhile a small circle is inscribed in the semicircle. Given that $AD=AE$ and theradiusof the quarter circle is $14\sqrt{2} \text{ cm}$ , find the area of the green region above (in $\text{cm}^{2}$ ).

For your final step, use the approximation $\pi = \dfrac{22}{7}$ .

I begin with a circle of radius $1 \text{ cm}$ , which becomes the inscribed circle of an equilateral triangle, which I enclose with its circumcircle (the circle that touches all of its vertices). I enclose this circle with a square (so that each edge touches the circle once), and surround this with the square's circumcircle. I repeat this procedure with a pentagon, a hexagon, and so on forever (increasing the side number by one, until we reach an infinity-sided polygon).

What is the limiting area (in $\text{cm}^2$ ) of the "final" circle, rounded to a whole number?

$ABCD$ is a square with points $E$ and $F$ lying on sides $CD$ and $AD,$ respectively. If the purple area is $[BHGI]=120,$ what is the sum of the pink areas $(AHF) + (fg) +[ICE]?$

What is the area of the large square?

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Composite Figures: Level 3 Challenges