At the rate of $2.00 per square foot, the cost of painting the rectangular board with a semicircular top shown in the figure is $.

it consists of a rectangle, dimensions L = 4ft and W = 3ft = Ar = 4ft x 3ft = 12 ft^2

then, you have one half of the area of the circle that has diameter R = 3ft - radius will be r = 1.5ft the area of that half will be:

Ac = r^2 / 2

= (1.5 ft) ^2 x 3.14 / 2

= 2.25 ft^2 x 3.4/2

= 7.065 ft^2 / 2

= 3.5325ft^2

A = Ar + Ac

A = 12ft^2 + 3.5325ft^2

A = 15.5325ft^2

At the rate of $2 per square foot, the cost will be:

$ 15.5325*2 = 31.07