Giving multiple links to an image

Ordinary image maps are not responsive on all devices.  The hotspot coordinates invariably drift out of register when the photo is rescaled. 

One way to avoid this problem is to not use an image map.  Instead, use individual linked  images.

A second way around this problem is to create an image map with SVG code instead of HTML code.   Below is a working example using simple shapes as hotspots on top of a raster background image.

https://jsfiddle.net/NancyO/6k3v4ge1/13/

Things to check...

1. Are you in Design View?
You will not see the Image Map tools in the Properties window while in Live View.

2. Is the image selected?
The Image Map Tools are not available until the image is selected.

3. Is your Properties window expanded?
There is a tiny triangle on the right side of the Properties window, that needs to be pointing up to fully expand the window and expose the Image Map tools.

This should help How to include interactive hotspots in your web site