Question

A window is being replaced with tinted glass. The plan below shows the design of the window. Each unit length represents 1 foot. The glass costs $12 per square foot. How much will it cost to replace the glass? Use 3.14 for π.

Answer 1

The image of the window can be seen below:

In the image we can see that the window can be separated in:

One rectangle of 4ft by 5 ft

Two half-circles (that if we add we get a complete circle) of diameter D = 4in.

First, we know that for a rectangle of length L and width W, the area is:

A = L*W

Then the area of our rectangle is:

A = 4ft*5ft = 20ft^2

And for a circle of diameter D, the area is:

A' = 3.14*(D/2)^2

In this case we have D = 4in, then the area of the circle (that we get when we add the areas of the two half-circles) is:

A' = 3.14*(4ft/2)^2 = 3.14*4 ft^2 = 12.56 ft^2

Then the total area of the window is:

Area = A + A' = 20 ft^2 + 12.56 ft^2 = 32.56 ft^2

And we know that each square foot of glass costs $12, then 32.56 square foots of glass will cost 32.56 times $12

Then the total cost is:

C = 32.56*$12 = $390.72