Answer:
[tex]36+27\pi\:\mathrm{in^2}[/tex]
Step-by-step explanation:
The figure consists of a square and a sector. We can add the areas of the square and sector to get the total area of the figure.
The area of a sector with measure [tex]\theta[/tex] in a circle of radius [tex]r[/tex] is equal to [tex]\frac{\theta}{360}\cdot r^2\pi[/tex]. Since there are 360 degrees in a circle and 90 degrees in each corner of a square, the measure of the sector is [tex]270^{\circ}[/tex].
Thus, its area is:
[tex]\frac{270}{360}\cdot6^2\cdot pi=\frac{3}{4}\cdot 6^2\cdot \pi=27\pi[/tex].
The area of a square with side length [tex]s[/tex] is given by [tex]s^2[/tex]. Therefore, the area of the circle is [tex]6^2=36[/tex] and the total area of the figure is [tex]\boxed{36+27\pi\:\mathrm{in^2}}[/tex]
