For this case we have that the area of the figure is given by the area of a rectangle plus the area of a square. By definition, the area of a rectangle is given by:
[tex]A = a * b[/tex]
According to the figure we have:
[tex]a = 9 \sqrt {2}\\b = 8 \sqrt {2} -2 \sqrt {2} = 6 \sqrt {2}[/tex]
So, the area of the rectangle is:
[tex]A = 9 \sqrt {2} * 6 \sqrt {2} = 54 (\sqrt {2}) ^ 2 = 54 * 2 = 108[/tex]
On the other hand, the area of a square is given by:
[tex]A = l ^ 2[/tex]
Where:
l: it is the side of the square
According to the figure we have:
[tex]l = 2 \sqrt {2}[/tex]
So:
[tex]A = (2 \sqrt {2}) ^ 2 = 4 * 2 = 8[/tex]
Finally, the area of the figure is:
[tex]A_ {t} = 108 + 8 = 116[/tex]
Answer:
116
