A regular octagon is inscribed in a circle whose diameter measures 24 inches.

Mathematics
Tutor: None Selected Time limit: 1 Day

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.

May 9th, 2015

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


Let me know if you need further help. 


May 9th, 2015

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