Let's consider the figure consisting of a rectangle ABCD and a triangle CDE.

The area of rectangle ABCD is given by the formula: Area = length x breadth.

Given that the length of the rectangle is 7 cm and the breadth is 4 cm, we can calculate the area as follows:

Area of rectangle ABCD = 7 cm x 4 cm = 28 cm².

Now, let's move on to the triangle CDE. The area of a triangle is given by the formula: Area = (base x height) / 2.

Given that the area of triangle CDE is 12 cm², we can rearrange the formula to find the base or height:

12 cm² = (base x height) / 2.

Since the base and height are not explicitly given, we can't determine their values individually. However, we can use the fact that the base and height must multiply to give 24 cm² (twice the triangle's area).

Let's consider one possible combination:

base = 3 cm

height = 4 cm

Using this combination, we can calculate the area of triangle CDE as follows:

Area of triangle CDE = (3 cm x 4 cm) / 2 = 6 cm².

Now, to find the total area of the figure, we sum the areas of the rectangle and the triangle:

Total area = 28 cm² + 6 cm² = 34 cm².

Therefore, the total area of the given figure is 34 cm².