New answer.
I think I've got it now. You are a
picture frame.
I'm in your house, workplace, and more.
Some say I improve the decor.
True
To measure me, you measure twice,
But four times to be more precise.
You have to measure the outside of the frame twice (L x W) to see how much space on the wall it will need, and the inside of the frame twice (L X W) to see how large the picture can be/needs to be.
My pet's known for its speed.
Many picture frames use a rabbet on the back to hold the picture and backing.
My best friend's name is Matt.
Matting is critically important for a nice picture frame.
I'm usually quite thin,
But can be rather fat.
True. There are some seriously chunky picture frames out there.
The name of my main strength-
It happens to some food.
The strength of a picture frame is its molding/moulding. Molding also happens to some food if it sits around long enough, especially food with high moisture content.
One look at my contents
Can lighten up your mood.
Seeing my family's smiling faces makes me happy.
I endure falls and beatings and bangings.
I'm thinking of the pictures in our stairwell that I occasionally bump off the wall and they go cartwheeling down the stairs. They survive a couple of times, and then I have to glue them back together.
I've even been known to survive hangings.
Pictures often get hung on the wall.
So spend time with me if you're feeling down.
I will make a big smile out of that frown.
What's that old song about memories and reminiscing about stuff?
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Original Answer
I believe you are a
rug.
I'm in your house, workplace, and more.
Some say I improve the decor.
That's true.
To measure me, you measure twice,
But four times to be more precise.
You measure a rectangular rug in length and width, but you also have to measure the space for it so four total measurements.
My pet's known for its speed.
Rug rats (crawling) are shockingly fast.
My best friend's name is Matt.
Or mat (like a door mat)
I'm usually quite thin,
But can be rather fat.
Most rugs are thin, but some shag or ultra plush rugs are thick
The name of my main strength-
It happens to some food.
Rugs are tough. Unfortunately, that happens to food sometimes too.
One look at my contents
Can lighten up your mood.
Mood (or moud) rugs are a style of persian rug with lovely patterns in the weave.
I endure falls and beatings and bangings.
Fall down on a rug, no problem. Beat and bang it to clean it, also no problem.
I've even been known to survive hangings.
Some rugs are hung as decorations like a tapestry.
So spend time with me if you're feeling down.
Literally down on the floor.
I will make a big smile out of that frown.
Who doesn't like laying on the carpet sometimes?
