Explanation:
we need to find right-angled triangles, rectangles and squares with vertexes on grid dots. we calculate the different areas and then sum them up.
I see on the left a 1×2 right-angled triangle.
then connecting to that at the bottom a 3×1 right-angled triangle.
connecting to that on the right is another 3×1 right-angled triangle.
connecting to that on the top a 3×2 right-angled triangle.
and that left in the center a 2×1 rectangle.
remember, the area of a triangle is
baseline × height /2
the area of a rectangle is
length × width.
so, we have
1×2 / 2 = 1 unit²
3×1 / 2 = 1.5 unit²
3×1 / 2 = 1.5 unit²
3×2 / 2 = 3 units²
2×1 = 2 units²
in total that is an area of
1 + 1.5 + 1.5 + 3 + 2 = 9 units²