Get search results by relationship
Do another call to craft.entries when you loop through the "area" entries and include the section and relatedTo params:

{% for entry in searchEntries %}
    {% set videos = craft.entries.section('videoSectionHandle').relatedTo(entry) %}
    {% for video in videos %}
         {# Output video here #}
    {% endfor %}
{% endfor %}


If you're trying to maintain a one-to-one relationship it might make sense to limit the relation query to one result, and to include the first param to return the first (and only) result and not an array – then you can omit the nested for loop:

{% for entry in searchEntries %}
    {% set video = craft.entries.section('videoSectionHandle').relatedTo(entry).limit(1).first() %}
    {{ video ? #--Output video here--# }}
{% endfor %}


You can read more about the relatedTo param here, it's pretty powerful.