A square has side lengths of 24 cm. It is divided into four equal sections (as shown in the first picture) and then two of those sections are shaded. One of the unshaded sections is then divided into four equal sections and two of those are shaded (as shown in the second picture)

To find the total area shaded in the given square, we need to calculate the area of the original shaded sections and the additional shaded sections.

Let's break down the process step by step:

Step 1: Calculate the area of the original square
The side length of the square is given as 24 cm. To find the area of a square, we can use the formula: Area = side length * side length.
Thus, the area of the original square is 24 cm * 24 cm = 576 cm².

Step 2: Calculate the area of the original shaded sections
Since the square is divided into four equal sections and two of them are shaded, both shaded sections cover half of the original square.
Therefore, the area of each shaded section is 576 cm² / 2 = 288 cm².

Step 3: Calculate the area of the unshaded section
Since one of the unshaded sections is divided into four equal sections, and two of them are shaded, each shaded section covers one-fourth of the original unshaded section.
Thus, the area of each new shaded section is 288 cm² / 4 = 72 cm².

Step 4: Calculate the total area of the additional shaded sections
Since two of the new shaded sections are created by dividing the unshaded section, we have a total of 2 * 72 cm² = 144 cm².

Step 5: Calculate the total shaded area
To find the total shaded area, we need to sum up the areas of the original shaded sections and the additional shaded sections.
Total shaded area = Area of original shaded sections + Area of additional shaded sections
Total shaded area = 2 * 288 cm² + 144 cm² = 720 cm².

Therefore, the total area shaded in the given square is 720 cm².