I need to join these two shapes together to form something that looks like the back part of an AK47.
Thanks.
One way with native tools:
Draw the far shape.
Pushpull it to the distance of the near shape.
Select the upper rounded part of the near end. Scale on red/blue about centre (press Ctrl - Option on Mac) to enlarge it.
The sides will distort into two or more planes. Smooth’/soften edges to remove the hard lines.
Looks like this.
That good enough?
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It looks good enough but what do you mean by scale on red/blue?
Window select the upper near curve, or click it to select the arc that forms it.
Press S for scale.
Click on the top right grip of the Select tool, and press Ctrl to scale about the centre of the selection. That is ‘scale on the Red/Blue axes’. Drag that grip to get the shape you want, or type values for red (x) and a (blue) relative scaling - for example 2.0,2.5 - or final dimension if you specify length units - for example 1.5", 1.2" or 38mm, 38mm.
PS. Forgot to say, first scale the whole of the far end down to the size you want for the far end, or alternatively, scale up the near end .
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I’m not able to make it work the way you describe it but it’s probably because on the near end part it is hollow and I don’t know how to change that. But it’s not a problem right now. Thank you for your help, I will check back to your answers when I want to complete it. 
I’ll try to record a gif, later, but not tonight - it’s after 1am here.
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Thank you! 1am for me too 
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