A regular octagon is inscribed in a circle whose diameter measures 24 inches. Find, to the nearest hundredth, the area of the region wounded by the circle and the octagon.
Attached is the diagram which shows an octagon inscribed in a circle and calculation of its side. WP_20150510_001.jpg
Area of a circle = pi* r^2
here radius = 24/2 = 12 inches
Area of circle = pi*12*12 inch square = 452.16 inch square
Area of regular octagon = 2* (1+ square root of 2) * side^2
Area of regular octagon = 407.25 in sq
Therefore the area of the region wounded by the circle and the octagon = area of circle - area of octagon
= 452.16 - 407.25 inch square
area of wounded region = 44.9 inch square
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