The figure ABCDE shown in the diagram consists of a large square ACDE standing on the diagonal [AC] of a smaller square ABCF - Leaving Cert Mathematics - Question (b) - 2021

The area of the figure ABCDE can be calculated using the formula for the area of a square:

$\text{Area} = \frac{1}{2} \times (\text{side length of square ACDE}) \times (\text{height from A to C})$

The height from point A to C is equal to the length of the diagonal |AC|:

$\text{Area} = \frac{1}{2} \times (2 \times 2) = 2 \times \sqrt{8} = 10 \text{ cm}^2$

The perimeter of figure ABCDE can be found by adding all the sides:

$\text{Perimeter} = 2 + 2 + |AC| + |CD|$ Since |CD| is also 2 cm, we have:

$\text{Perimeter} = 2 + 2 + 2 + 2\sqrt{2} = 4 + 2\sqrt{2}$

Calculating it numerically, we find:

$\text{Perimeter} \approx 4 + 2 \times 1.414 = 4 + 2.828 = 6.828 \text{ cm}$

Therefore, rounding to two decimal places, the perimeter is approximately 12.49 cm.