1.

In Figure, two circular flower beds have been shown on two sides of asquare lawn ABCD of side 56m. If the centre of each circular flower bed isthe point of intersection of the diagonals of the square lawn, find the sumof the areas of the lawns and the flower beds.

Answer» We know that the diagonals of a square bisect each other perpendicularly
`:. Angle DOC = 90^(@)`
Also, diagonal BD = side `sqrt2 = 56 sqrt2 m`
`:. OD = (1)/(2) xx BD = 28 sqrt2 m`
`:.` Area of `Delta DOC = (1)/(2) xx 28 sqrt2 xx 28 sqrt2 = (28)^(2) m^(2)`
Area of sector ODCO `= pi (OD)^(2) xx (theta)/(360^(@))`
`= pi (28sqrt2)^(2) xx (90^(@))/(360^(@)) = (11 xx 28 xx 28)/(7) m^(2)`
`= 1232 m^(2)`
`:.` Area of 1 flower bed = Area of sector - Area of `Delta`
`:.` Area of 2 flower beds = `2 xx 448 = 896 m^(2)`
Area of square lawn `= (56)^(2) = 3136 m^(2)`
`:.` Required area `= 896 + 3136 = 4032 m^(2)`


Discussion

No Comment Found

Related InterviewSolutions