Question 15100
I can't draw any pictures on this, but we know that if you're looking at the north side of the house the highest point of the roof will be (1/2)*18 = 9 feet.

Since the slope is 4 in 12 we know the roof rises 4" for every foot of run or 1 foot for every 3 feet of run.
So for 9 feet of run the total rise of the roof is 3 feet.
So to solve for the length of the diagonal side we use the pythagorean theorem.
{{{9^2+3^2}}} = {{{diagonal^2}}}
90 = {{{diagonal^2}}}
{{{sqrt(90)}}} = diagonal
To figure out how many shingles we need, we need to find total area on the roof. the area of one half the roof is {{{sqrt{90)*28}}}, but we need the area of the full roof + 9 inches of overhang on all sides.  Note 9 inches = 3/4 of a foot.
So the area is 2[area of one-half the roof]
2[{{{sqrt(90)+(3/4)}}}*{{{28+(3/4)}}}
= 588.6178964
Now, 1 square of shingles will cover 100 square feet.
so we need 5 squares for 500 square feet and extra to cover the extra 88.6178964
So to be safe, she should order 6 squares of shingles or 600 square feet.
Hope the lack of pictures doesn't get you mixed up.