Question

At $10.19 per foot for the curved portion and $1.12 per foot for the straight portion, how much will it cost to put molding around the window pictured? Use x=3.14(Simplify your answer. Round to the nearest cent as needed.)

Answer 1

To answer this question we must compute the perimeter of the given figure.

Now, to compute the perimeter we divide the given figure into a rectangle and a semicircle, the radius of the semicircle is 2'9'', therefore its diameter is the same as the width of the rectangle is 2x2'9''. The length of the rectangle is 5'3''.

Recall that the perimeter of a semicircle is given by the following formula:

`P_c=\pi r\text{.}`

Substituting π=3.14 and r=2'9''=2.75' we get:

`P_c=3.14*2.75^(\prime)=8.635^(\prime).`

Now, the perimeter of the rectangle without including the upper side is:

`P_r=(5.25+5.25+5.5)^(\prime)=16^(\prime).`

Therefore, since the cost of molding the curved part is $10.19 per foot and we have 8.635', and the cost of molding the straight portion is $1.12 per foot and we have 16', then the total cost is:

`T=10.19*8.635+1.12*16=87.99065+17.92=105.91065\approx105.91.`

Answer: $105.91