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Question
Calculate the area of the designed region in the given figure common between the two quadrants of circles of radius 8 cm each. [Use Π = 22/7]
Solution
The designed area is the common region between two sectors BAEC and DAFC.
Area of sector BAEC = `90^@/360^@ xx 22/7xx(8)^2`
`=1/4xx22/7xx64`
`=(22xx16)/7 cm^2`
`= 352/7 cm^2`
Area of ΔBAC = `1/2xxBAxxBC`
`= 1/2xx8xx7 = 32 cm^2`
Area of the designed portion = 2 × (Area of segment AEC)
= 2 × (Area of sector BAEC − Area of ΔBAC)
`= 2xx(352/7 - 32) = 2((352-224)/4)`
`= (2xx128)/7`
`= 256/7 cm^2`
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