Answer:
9.5 square units
Explanation:
You want the area of the shaded shape bounded by diagonals in a figure composed of two squares.
Pick's theorem
When a shape is bounded by lines on a grid, the area of the shape can be found by counting boundary grid points (b) and interior grid points (i). The area is ...
A = i + b/2 -1
In the attached figure, the 11 boundary points are identified by the larger blue dots, and the 5 interior points are identified by the smaller red dots. Using these numbers, the area is found to be ...
A = 5 +11/2 -1 = 9.5 . . . . square units
(Blue points marked A and E are not counted in the boundary of the shaded shape.)
Addition and Subtraction
We can also find the area of the shaded shape by subtracting the unshaded areas from the total area of the two squares.
The 3×3 square and the 5×5 square have a total area of ...
3·3 +5·5 = 9 +25 = 34 . . . . square units.
The upper unshaded triangle has an area of ...
A = 1/2bh = 1/2(5)(5) = 12.5 . . . . square units
The lower unshaded triangle has an area of ...
A = 1/2bh = 1/2(8)(3) = 12 . . . . square units
The area of the shaded figure is the total area less the unshaded area:
A = 34 - 12.5 -12 = 9.5 . . . . square units
The area of the shaded shape is 9.5 square units.