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

Draw a \(1\text{ m}\) by \(1\text{ m}\) square.

Then inscribe the largest possible circle within the square previously drawn.

Then inscribe the largest possible square within the circle previously drawn.

Then inscribe the largest possible circle within the square previously drawn.

Then inscribe the largest possible square within the circle previously drawn.

Then repeat the process indefinitely.

What will be the total area of all the squares drawn (in \(\text{m}^2\))?

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The above figure shows five congruent rectangles. A trapezoid is drawn in such a way that its vertices coincide with vertices of some of the rectangles. What percentage of the figure is shaded?

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A square and a "Shuriken" (throwing star) figures are drawn over the \(5\times 5\) dot grid as shown above.

Which colored region has more area?

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I cut out 4 rectangles from each of its corners as shown above.

What is the perimeter of this new figure?

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The figure above shows three consecutive squares of sides 5, 4 and 3, respectively.

Find the area of the black region.

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