If there was a triangular prism connected to a base flared cylinder, how would you calculate the volume?

Thank you! 

I think that you need to describe the shape better than that.

but

you would probably find the volumes seperately and add them together.

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I do not know where you got the trinagular prism from but if I wanted to know the volume of that vase this is how I might do it.

[I am going to find the volume by measuring the displacement of water]

1) I'd seal the vase so it was airtight - maybe with strong cling wrap and tape.

2) I'd put the vase inside of a slightly bigger waterproof container.

3) I'd pour water into the outer container untill it covered the vase. 

4) I'd put a mark on the outer container to indicate where the water reached.

5) I'd then remove the vase from the container but I'd leave the water behind.

    The water level has now dropped by the volume of the vase. 

6) Add more water to the outer container container, measuring it as it was added, untill the water reached the original level again.

7) the amount of extra water that you added will be the volume of the vase. 

$$1cm^3 = 1ml$$         so the conversion from capacity to volume is really easy.

     Say you got   $$1200ml$$    This is equivalent to     $$1200 cm^3$$

https://www.youtube.com/watch?v=n3ia4i-uFTM