Textured ceiling repair

I have a small area of damage in my kitchen ceiling from a water leak in the bathroom above. The leak is repaired, but the water created a crumbly hole about 6" in diameter. The ceiling is coated with a texture about the size of small-curd cottege cheese. How best to patch the hole?
My idea is to cut out a 1-foot square hole where the damage is. Then I'll make a 1-foot patch out of wood or wallboard and hang it inside the hole with wooden supports (this was suggested to me by a friend.) Now I'm wondering how to camouflage the patch. Can I use drywall tape and spackle/plaster to hide the seam? Can you buy small amounts of the texture to brush or spray on the smooth patch? I expect the patch will never be invisible, but I'd like it to be as unnoticable as I can.
Any advice or suggestions would be greatly appreciated.
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Nil wrote:

Fairly common way to do it. Just keep it as small as possible.

Yes, tape the seam and then use a spray can of the texture stuff, which you can purchase at your local hardware store or building supply center of choice. The biggest challenge is getting the two different whites to blend. Feathering the edge of the new section onto the old usually works fairly well.
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The current textured stuff looks like it was applied with a brush or trowel, since I can see distinct swirl patterns. I wonder if I can get brush-on stuff - I think spray-on would look quite different. I've seen some spray-on, but it looked like it goes on in larger "curds" than what I have. I guess I need to check out what's available.
Thanks very much for the advice.
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I bought some texture in a tube that has a sponge built in at the end. Worked fantastically and matched an 8 year old ceiling when dry. Bought at LOwes or Home Depot. You shake the tube and then squeeze the stuff up thru the built in applicator and dab it on. Could probably make swirl marks after if you wanted to but wasn't an issue for me.

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The texture you'll are matching - is this the same as the popcorn finish? I've got several areas that need to be "redone"....just didn't know what to get.
Dorothy
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Nil wrote:

Oh, now that you gave those details. Yes, you can buy it in a non-spray form too.
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I went to Home Depot today and they have some texture that you mix with paint. It's hard to tell from the small picture on the box, but I think that will more closely match what's on the ceiling now than the spray- on.
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