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That depends on the roof material. Metal can be as low a 1/12. Fibergglass shingles should be at least 3/12.
3 inch per foot is usually the lowest pitch for shingles. For only 1/4 inch slope, rolled roofing should be used.
patio
A great option is to use overhead spotlights or torch lights that are mounted on the side or roof of your house. If you have a patio roof you can also mount lights on the patio roof itself
I don't think an umbrella should be used on a balcony of that size. A roof cover would probably be a better choice, like a cover that can extend from a wall.
do grants cover windows and roof
It should cover your roof for accidental damage, it will not cover a new roof if it needs replacing due to age.
A single pitch roof is basically a flat roof with a pitch (or angle), usually to allow water to run off. This differs from a double pitch roof /\ that is what you commonly see.
Roof pitch is measured in "rise over run". In other words, how many inches does the roof rise vertically in 12" of horizontal run. If a roof rises 4" in 12" of run, you have a 4/12 roof pitch.
Roof pitch is measured in "rise over run". In other words, how many inches does the roof rise vertically in 12" of horizontal run. If a roof rises 4" in 12" of run, you have a 4/12 roof pitch.
Lots of people do. Google search, "Patio Builders" Landscaping contractors also build patios. These patios come in concrete, brick, pavers, flagstones etc. You can also ask contractors to build a covered patio. This may be a pergola or ceiling/roof type of cover.
Roof pitch is rise and run. So if you have a 4/12 pitch, for every foot of run the roof rises 4 inches.