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# Geometry Warmups

Mathematics is filled with shapes that are kaleidoscopic in variety. Wielded since ancient times, the power of geometry helps us examine and measure these shapes.

# Composite Figures Warmup

$$A, B, C, D$$ are equally spaced points on a line. Semicircles are constructed on both sides, and colored in, as in the above image.

Which region is the smallest?

To draw an alien's head, Mary drew a large circle, and then added 2 equal black circles for the eyes. She colored the smaller circles black, and colored the rest of the figure grey.

Which region is larger, the grey region or the black region?

There is a garden (the green part of the image) that measures 4 feet by 6 feet. All around it, a path that measures 1 foot wide is constructed. What is the area (in square feet) of the path?

In the above square of side length 2, we draw in 2 quarter circles and shade them blue and red respectively.

What is the area of the purple oval region, where these quarter circles overlap?

The above blue cross is formed by two 2 by 7 rectangles. What is its area?

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