The following is the complete solution to the above problem:
looking at the figure, we can see that the curve on both sides are two-quarter circles with radius a each.
therefore, the perimeter of the figure = (1/4)*2π*a + b + (1/4)*2π*a+ a + b + a = πa + 2a + 2b = 160 => πa/2 + a + b = 320
Area of the figure = 2* area of quarter circles + area of rectangle = 2(1/4)*π * a² + ab = π/2*a²+ab = A
(A + a²)/a = A/a + a = aπ/2+b + a = 320