Is audio supported through the VGA connection of the adapter?

No, the VGA connection does not support audio, while the DisplayPort supports 7.1 channel audio.

What resolutions does the StarTech.com DisplayPort to HDMI VGA Adapter support?

The adapter supports DisplayPort resolutions up to 3840x2160 (4K) at 60Hz and VGA resolutions up to 1920x1080 at 60Hz.

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StarTech.com DisplayPort to HDMI VGA Adapter - 4K 60Hz - Multiport Video Converter for Mac & Windows - Male to Female (DP2VGAHD20)

Use this 2-in-1 DisplayPort to HDMI VGA adapter to maximize your laptop’s video compatibility
This DP to HDMI VGA converter can support resource-demanding applications with support for UHD resolutions up to 4K 60Hz - Perfect for professionals on the go, this compact and lightweight DisplayPort video adapter can easily fit in your laptop bag
This DisplayPort (male) to HDMI VGA (female) dongle supports plug & play connectivity, removing the need for additional drivers and software