Filtering search with checkboxes multiple param querystring
You can do this by getting all the params in the url that have the same name and joining them into a single string which you can use in your Twig template.

Note this code is untested but is based on something I've recently done. This example only uses categories but it's possible to expand it to search custom fields and/or add a free text search too.

{# get all the area params and join them into a comma delimited string %}
{% set areaQuery = craft.request.getParam('area') | join(',')  %}


{# build the search query #}
{% set relatedParams = ['and'] %}


{% set areas = craft.categories.group('areas').slug( areaQuery | split(',') ).find() %}
{% for area in areas %}
    {% set relatedParams = relatedParams|merge([{ targetElement: area }]) %}
{% endfor %}


{# execute the search and get a resultset of entries #}
{% set entries = craft.entries.relatedTo(relatedParams).order('score') %}

{# output your entries #}