Rotating Square​

 

 

 

 

 

 

 

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The dot represents the center of the square. Find the position of the blue square such that the overlapping area (as a fraction of the orange square's area) is maximum. 

Circle, Square, Circle

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The blue quadrilateral is a square. What is the ratio of the two circles' areas? 

Four Arcs and a Square

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All arcs are congruent. What is the area contained by the four arcs as a fraction of the square's area?

Circles vs. Squares

 

 

 

 

 

 

 

The two large circles have radii of 1. The dodecagon is made up of five squares. Which design contains the largest area: the four circles or the dodecagon? 

3 Vertices, 2 Midpoints

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The blue segments connect a vertex to the midpoint of a side. What fraction of the square's area is yellow?

4 Vertices, 4 Midpoints​

 

 

 

 

 

 

 

 

The blue segments connect a vertex to the midpoint of a side. What fraction of the square's area is yellow?