To determine the area of the figure composed of 3 identical triangles, follow these steps:

Given:

1. The total height of the figure is 30 cm.
2. The total width at the bottom is 20 cm.
3. The figure consists of 3 identical triangles.

Step-by-Step Solution:

Step 1: Understand the triangle arrangement

The figure is made of 3 identical triangles arranged such that:

• The total height of the figure (30 cm) spans 2 triangle heights (each triangle contributes half its height to overlap).
• The base of each triangle is given as 20 cm.

Step 2: Calculate the height of one triangle

• Let the height of one triangle be $h$.
• Since the total height equals 2 triangle heights: $2h = 30 \, \text{cm} \quad \implies \quad h = \frac{30}{2} = 15 \, \text{cm}.$

Thus, the height of one triangle is 15 cm.

Step 3: Calculate the area of one triangle

The area of a triangle is given by: $\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}.$

• Base = $20 \, \text{cm}$
• Height = $15 \, \text{cm}$

Substitute these values: $\text{Area of one triangle} = \frac{1}{2} \times 20 \times 15 = 150 \, \text{cm}^2.$

Step 4: Calculate the total area of the figure

Since the figure is composed of 3 identical triangles: $\text{Total Area} = 3 \times 150 = 450 \, \text{cm}^2.$

Final Answer:

The area of the figure is 450 cm².

Let me know if you would like further clarification or additional details!

Related Questions:

1. What is the perimeter of the figure?
2. How would the area change if the base of each triangle were doubled?
3. Can you calculate the area of a single triangle using a different method, such as trigonometry?
4. What is the relationship between the height of the triangles and their arrangement in the figure?
5. How would the figure's area change if it consisted of 4 identical triangles instead?

Tip: Remember that the total height and width of composite figures can often give clues about individual shapes.