Use a ruler and compass.

a. Draw AB with a length of 1 inch. Open the compass to 1 inch and draw a circle with that radius. Using the same compass setting, mark off equal parts along the circle. Then connect the six points where the compass marks and circle intersect to draw a regular hexagon as shown. 

b. What is the area of the hexagon? of the shaded region? 

c. Explain how to construct an equilateral triangle.

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A B