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 $?

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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