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Why are the lower deck areas shaped like that, does that save some space? I find it common across lot of big aircraft.

Pic of a 777: 777 Cargo Compartment

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The answer lies in the existence of something called a Unit Load Device (ULD) -- basically a cargo pod for aircraft that's the equivalent of the shipping pallet.
ULDs allow oddly-shaped cargo (bags, assorted-size boxes, etc.) to be loaded efficiently in a standard volume and easily secured for flight (using hold-down lugs in the floor).

The shape of the cargo deck is designed to pack in as many ULDs as possible:
A300 cross-section with ULDs
and as you can see from the cross-section the sloping sides on the bottom are a concession to the circular cross-section of the fuselage/pressure vessel.

Some other advantages of ULDs as they pertain to airline operations and baggage loading are described over on this question.

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  • $\begingroup$ Why not expand the cargo compartment to use the whole bottom half? $\endgroup$
    – user253751
    Aug 6, 2015 at 23:57
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    $\begingroup$ There are a number of systems (e.g., power, flight controls, environmental ducts) routed through the spaces alongside & under the cargo area. $\endgroup$
    – Ghillie Dhu
    Aug 7, 2015 at 1:46
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    $\begingroup$ @immibis: Standardization. It's more economical to use a standard part for all aircraft than require each type of aircraft to use different containers. Conceivably, when ULDs were invented they use a higher % of the cross section of the average airliner. Nowdays widebodies are common so they end up using a smaller % of the cross-section. $\endgroup$
    – slebetman
    Aug 7, 2015 at 3:39
  • $\begingroup$ @immibis I'm not sure what you mean by "the whole bottom half" -- are you saying just throw things into the bottom half-cylinder of the fuselage? If so, how will you accomplish the loading? (Hint: "Throw everything in there loose" doesn't work: It's inefficient in both space and time, and has other problems detailed in the post I linked to.) Similarly having half-cylinder ULDs doesn't work (they're too difficult to handle on the ground). ULDs trade a relatively small percentage of wasted space for enormous gains in cargo-handling efficiency. $\endgroup$
    – voretaq7
    Aug 7, 2015 at 6:53
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    $\begingroup$ @immibis: The bottom surface holds rails for quick loading. That's intentionally a horizontal surface. The space to the side is fairly small. $\endgroup$
    – MSalters
    Aug 7, 2015 at 9:35

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