WPF Square auto-size to parent container

Question

I have a UniformGrid object in my WPF project that has 2 rows and 3 cols and its width and height are set to auto (with both alignments set to Stretch).

This grid will hold 6 squares that I want to fill as much of their cell as possible and be centered horizontally and vertically.

What do I need to be added to allow for the squares to increase/decrease their length/width based on the dynamic size of the parent? I.E., when the window is resized.

Here is my xaml so far:

    <UniformGrid Rows="2" Columns="3">
        <Rectangle Fill="#FFF4F4F5" Height="100" Stroke="Black" Width="100"/>
        <Rectangle Fill="#FFF4F4F5" Height="100" Stroke="Black" Width="100"/>
        <Rectangle Fill="#FFF4F4F5" Height="100" Stroke="Black" Width="100"/>
        <Rectangle Fill="#FFF4F4F5" Height="100" Stroke="Black" Width="100"/>
        <Rectangle Fill="#FFF4F4F5" Height="100" Stroke="Black" Width="100"/>
        <Rectangle Fill="#FFF4F4F5" Height="100" Stroke="Black" Width="100"/>
    </UniformGrid>

Edit:

And the Rectangle objects need to remain square.

Answer 1

<Page xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation" xmlns:sys="clr-namespace:System;assembly=mscorlib" xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml" >
  <Grid>
<UniformGrid Rows="2" Columns="3">
<Viewbox Stretch="Uniform"><Rectangle Height="100" Width="100" Fill="#FFF4F4F5" Stroke="Black" /></Viewbox>
<Viewbox Stretch="Uniform"><Rectangle Height="100" Width="100" Fill="#FFF4F4F5" Stroke="Black" /></Viewbox>
<Viewbox Stretch="Uniform"><Rectangle Height="100" Width="100" Fill="#FFF4F4F5" Stroke="Black" /></Viewbox>
<Viewbox Stretch="Uniform"><Rectangle Height="100" Width="100" Fill="#FFF4F4F5" Stroke="Black" /></Viewbox>
<Viewbox Stretch="Uniform"><Rectangle Height="100" Width="100" Fill="#FFF4F4F5" Stroke="Black" /></Viewbox>
<Viewbox Stretch="Uniform"><Rectangle Height="100" Width="100" Fill="#FFF4F4F5" Stroke="Black" /></Viewbox>
    </UniformGrid>
  </Grid>
</Page>