The figure in the image appears to be a composite shape, which can be broken down into a larger triangle with a smaller triangle subtracted from it. The goal is to calculate the area of the shape by subtracting the area of the smaller triangle from the area of the larger triangle.

Step 1: Calculate the area of the larger triangle

The larger triangle has:

• A base of 10 cm.
• A height of 12 cm.

The area of a triangle is given by the formula: $\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$ So, for the larger triangle: $\text{Area}_{\text{large}} = \frac{1}{2} \times 10 \, \text{cm} \times 12 \, \text{cm} = 60 \, \text{cm}^2$

Step 2: Calculate the area of the smaller triangle

The smaller triangle has:

• A base of 5 cm.
• A height equal to the difference between the height of the larger triangle and the height of the figure itself.

Given that the entire height of the figure is 12 cm and that the small triangle lies directly under the top vertex, we can observe the small triangle has half the height of the full figure:

• Height of the small triangle = 12 cm / 2 = 6 cm.

So the area of the smaller triangle is: $\text{Area}_{\text{small}} = \frac{1}{2} \times 5 \, \text{cm} \times 6 \, \text{cm} = 15 \, \text{cm}^2$

Step 3: Calculate the area of the figure

Now, subtract the area of the smaller triangle from the area of the larger triangle: $\text{Area}_{\text{figure}} = \text{Area}_{\text{large}} - \text{Area}_{\text{small}} = 60 \, \text{cm}^2 - 15 \, \text{cm}^2 = 45 \, \text{cm}^2$

So, the area of the figure is 45 square centimeters.

Would you like further details on any of the steps? Here are some related questions you might find helpful:

1. How would the area change if the smaller triangle had a different height?
2. What would be the area if both triangles were equilateral?
3. How would you calculate the perimeter of the figure?
4. What is the formula for the area of a trapezoid, and how does it compare to this method?
5. How can you verify the height of the smaller triangle using trigonometry?

Tip: When breaking down composite shapes into simpler shapes, ensure each component's dimensions are clearly identified to avoid miscalculations.