Q. 33.7( 6 Votes )

A regular hexagon of side 10 cm is cut from a plane circular sheet of radius 10 cm as shown in the figure 13.11. Find the area of the remaining part of the sheet. ( = 1.73) (= 3.14)



Answer :

Given radius of the circle (r) = 10 cm


Side of the hexagon (a) = 10 cm


we can divide the hexagon into 6 equilateral triangles as follows.



the side of an equilateral triangle will be 10 cm


we have to find the area of the shaded region as shown in fig. 13.11


area of the shaded region = area of circle - area of hexagon


= area of circle - area of 6 right equilateral triangles


= π r2 – 6 ()


= 3.14 × 102 – 6 ( × 102)


= 54.5 cm2


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