The shape in the image is a triangle. To find its area, we use the formula for the area of a triangle:

$\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}.$

Step-by-step Solution:

1. The base of the triangle is $\frac{2}{5} \, \text{cm}$, as labeled in the image.
2. The height of the triangle is also $\frac{2}{5} \, \text{cm}$, as shown by the dashed line perpendicular to the base.

Now substitute these values into the formula:

$\text{Area} = \frac{1}{2} \times \frac{2}{5} \times \frac{2}{5}.$

Calculate:

$\text{Area} = \frac{1}{2} \times \frac{4}{25} = \frac{4}{50}.$

Simplify $\frac{4}{50}$ to its lowest terms:

$\text{Area} = \frac{2}{25} \, \text{square centimeters}.$

Final Answer:

The area of the triangle is:

$\boxed{\frac{2}{25}} \, \text{square centimeters}.$

Do you want more details or have questions about this?

Here are 5 related questions to explore:

1. How do you simplify fractions like $\frac{4}{50}$?
2. What is the formula for the area of other geometric shapes, such as rectangles or circles?
3. How would the area change if both the base and height doubled?
4. What is the relationship between the height and base of a triangle in this type of problem?
5. How can you calculate the area if the height isn't perpendicular to the base?

Tip: Always ensure units are consistent when solving geometry problems!