If my area is 12x26 will the 16x20 provide enough shade?

With information provided it is impossible to give you an answer. It all depends on where you want the shaded area in relation to sun location. For example early in the morning the sun is rising from the east therefore there will be shade on the west side of the sun shade, in the afternoon it will be the opposite (shaded area in the east). It also depends on how high your shade is located from the floor, the higher the less shaded area under the sun sail. At noon since the sun at 12:00 o'clock PM., you get maximum shade under the sun sail. The shade under the sun sail is in relation to the angle of the sun in relation to 12:00 o'clock PM. or perpendicular to the floor. If you hold an object (card board box, piece of plywood, etc) at different timed during the day, you can see how the shaded area moves in relation to the sun location. Hope this helps some, you can also hang a bed sheet to get an idea of the shade under the sun sail at different times.

I have an area 18x23 to cover. Given the allowance for the ropes and stretching, what size rectangular sail should I get?

It all depends on where you want the shaded area in relation to sun location. For example early in the morning the sun is rising from the east therefore there will be shade on the west side of the sun shade, in the afternoon it will be the opposite (shaded area in the east). It also depends on how high your shade is located from the floor, the higher the less shaded area under the sun sail. At noon since the sun at 12:00 o'clock PM., you get maximum shade under the sun sail. The shade under the sun sail is in relation to the angle of the sun in relation to 12:00 o'clock PM. or perpendicular to the floor. If you hold an object (card board box, piece of plywood, etc) at different timed during the day, you can see how the shaded area moves in relation to the sun location. Hope this helps some, you can also hang a bed sheet to get an idea of the shade under the sun sail at different times.

How high does it need to be? Trying to cover a patio 20 x 23

I don't think there is a "need", obviously you need to be able to walk under it. I would think as high as possible. I used 12 foot 6x6 as corners, and sank them 3 feet into the ground. 2 sides are attached at the top, 2 are2.5 feet lower. My 6 foot son can walk under without a problem. Hope this helps.

Can I put this over a gas fire pit?

As long as the distance between the sail and table top gas fire pit is 4 feet or greater, you shouldn't have a problem, normally gas fire pits are controlled heat, so the heat doesn't fly more to 1-2 feet, I took my table top unit off otherwise I would have shared a picture. But if you go to reviews, I have pictures of the overall installation for this product and you can get an idea. My unit was installed at 100 inches a little over 8 feet on one side and 90 inches on the other side and a few inches under 8 feet for a gradual slope. The distance between my table top unit and the sail was approximately 4 1/2 feet when I measured.

Color	Cream
Size	8' x 12'
Style	Rectangle
Shape	Rectangular
Material Type	Polyethylene (PE)
Number of Items	1
Power Source	Manual
Features	UV-Blocking
Included Components	With 1. 5m hanging PE ropes (3 ropes for Triangle, 4 ropes for Rectangle/Square) Easy to set up with stainless steel D-rings at each corner
Brand	ASTEROUTDOOR
Manufacturer	AsterOutdoor
Item model number	Sun Shade Sail Rectangle 8' x 12'
Product Dimensions	365.76 x 243.84 x 0.25 cm; 1.7 kg
ASIN	B083CBMT8L

AsterOutdoor Sun Shade Sail Rectangle 6' x 10' UV Block Canopy for Patio Backyard Lawn Garden Outdoor Activities

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