Technically adipose tissue is areolar CT with adipocytes (fat cells) scattered within it. Adipose tissue can also be found near blood vessels and tightly packed underneath the skin forming the hypodermis (subcutaneous fat). Adipocytes are probably (in my opinion) the easiest to identify underneath a microscope because they look like ping pong balls packed together. Adipocytes have a round, white appearance to them. It looks like they do not have a nucleus but don't be fooled, it's there. The white inner part of the cell is oil or fat droplets. There is so much of that oil within adipocytes that all the other organelles, nucleus included, are pushed up against the plasma membrane. If you look closely you can usually spot the nucleus because an area of the membrane will look darker than normal.
Adipose tissue's main job is energy storage. You have to remember that we are animals and need to prepare ourselves for survival. During harsh conditions where food is not readily available we will tap into our fat to sustain life. The subcutaneous fat can also act as a cushion against impact against the body and is also a mild insulator for heat.
Brown fat is not really prevelant in humans, not for long anyway. This type of fat is brown because of the presence of mitochondria. This type of fat is metabolically active and is used to give off heat. This is very useful in hibernating animals who aren't active much during the winter time.
Source: The mind of Aaron
Here is an explanation of adipose tissue
Source: Self made with images from Marieb & http://www.udel.edu/biology/Wags/histopage/colorpage/colorpage.htm
Here are some images for you to study, try to find the nucleus within the adipocytes
Source: self made with images from http://www.udel.edu/biology/Wags/histopage/colorpage/colorpage.htm
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