Question

A lawn is in the shape of a semicircle of diameter 42m. the lawn is surrounded by a flower bed of width 7m all round. Find the area of the flower bed in m².

Answer 1

There are two concentric semi circles. The diameter of the inner circle = 42 or radius, a = 21m. The radius of the outer circle, b = 21 + 7 = 28m.

Because the radius of a Circle with diameter d is r = `"d"/(2)`

The Area of the inner Semi-circle with radius a = `(pi"a"^2)/(2) = (pi21^2)/(2)`

∴  The Area of the outer Semi-circle with radius b = `(pi"b"^2)/(2) = (pi28^2)/(2)`

and The Area of a Semi-circle with radius r = `(pi"r"^2)/(2)`

The Area of the flower bed 

= `(pi28^2)/(2) - (pi21^2)/(2)`

= `pi/(2)(28^2 - 21^2)`

= `pi/(2)(784 - 441)`

= `pi/(2)(343)`

= `(22)/(7 xx 2)(343)`
= 539m².