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The front of a metal shed needs to be spray painted. One can of spray paint will cover 20 square feet. If the 8ft x 8ft square door is not painted, then how many cans of spray paint will you need to buy?

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We know that each can can cover 20 square feet. Hence, we first need to calculate the total area we need to cover (shaded region).

The shaded region consists of the triangle and the rectangle.

For the rectangle:

`A = l*w = 16*10 = 160 sq.ft`

However, the square door will not be painted. The area of the square door is:

`A = s^2 = 8^2 = 64 sq.ft`

Hence, the shaded region within the rectangle is only:

`A = 160 - 64 = 96 sq.ft.`

For the triangle:

We first need to solve for x. Since the two legs both have length x and there is a right angle, this triangle is a 45-45-90 triangle. In a 45-45-90 triangle, we know that the legs can be solved as follows:

`l = h/sqrt(2) = 16/sqrt(2) = 8sqrt(2)`

Next, we consider the legs as the base and the height (for simplicity of calculation). The area then is:

`A = 1/2 bh = 1/2 (8sqrt(2)) * (8sqrt(2)) = 64 sq.ft.`

Hence, the total area we need to cover is:

`A_T = 96 + 64 = 160 sq.ft`

The number of cans we need is:

`n = (160sq.ft)/(20 (sq.ft)/(can)) = 8 cans`

Hence, we need 8 cans to finish painting.

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