Asquare rests inside a regular octagon. each shape has a side length measuring 9 inches. find the area of the shaded region, rounded to the nearest square inch. a. 310 in2 b. 162 ft2 c. 391 in2 d. 229 in2

Area of the octagon = 8 * side length^2 / [4 * tan (180/8)]
Area of the octagon = 8 * 9^2 / [4 * tan(22.5)]
Area of the octagon = 648 / 4 * 0.41421
Area of the octagon = 648 / 1.65684
Area of the octagon = 391.1059607446 square inches

Gray Area = 391.105 minus square area
Gray Area = 391.105 -81
Gray Area = 310.105 square inches

Source:
http://www.1728.org/polygon.htm
 

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