We will first determine the sides of 2 & 3, that is:
[tex]80=S^2_3\Rightarrow S_3=4\sqrt[]{5}[/tex]
And:
[tex]100=S^2_2\Rightarrow S_2=10[/tex]
Where S2 and S3 are the sides of squares 1 and 2. From this we determine the side for square 1:
[tex]S^2_2+S^2_3=S^2_1\Rightarrow(4\sqrt[]{5})^2+10^2=S^2_1\Rightarrow S_1=6\sqrt[]{5}[/tex]
Now, we determine the area of square 1, as follows:
[tex]A_{s1}=(6\sqrt[]{5})^2\Rightarrow A_{s1}=180[/tex]
So, we have that the area of square 1 equals 180 squared units.
