Let's analyze the problem step by step:

The figure consists of 7 congruent rectangles and 1 square. Each rectangle has a length of 5 cm and a width of 1 cm.

Step 1: Analyze the figure and dimensions

• Each rectangle has dimensions 5 cm (length) and 1 cm (width).
• The square is adjacent to the rectangles, and since the width of the square is equal to the width of the rectangles, the side length of the square is also 1 cm.

Step 2: Triangle fitting into the figure

We need to find the area of the largest triangle that can fit in this figure. Based on the figure's structure, the triangle will likely cover the entire height and width of the rectangle stack and the square.

The base of the largest triangle will be the total width of the entire structure. This is 5 cm (the length of each rectangle).

The height of the triangle will be the combined height of the 7 rectangles plus the square. Since the height of each rectangle is 1 cm and there are 7 rectangles, the total height of the rectangles is: $7 \times 1 \, \text{cm} = 7 \, \text{cm}$ Adding the height of the square (which is also 1 cm), the total height is: $7 \, \text{cm} + 1 \, \text{cm} = 8 \, \text{cm}$

Step 3: Area of the triangle

The area $A$ of a triangle is given by the formula: $A = \frac{1}{2} \times \text{base} \times \text{height}$ Substituting the base (5 cm) and height (8 cm): $A = \frac{1}{2} \times 5 \, \text{cm} \times 8 \, \text{cm} = \frac{1}{2} \times 40 \, \text{cm}^2 = 20 \, \text{cm}^2$

Final Answer:

The area of the largest triangle that can fit in the figure is $20 \, \text{cm}^2$.

Would you like a further breakdown or explanation of any part? Here are some related questions you might find useful:

1. How do you calculate the area of a triangle from different geometric shapes?
2. How would the area change if the dimensions of the rectangles were different?
3. What if the figure had more or fewer rectangles—how would that affect the triangle's area?
4. Can the largest triangle be rotated or positioned differently in this case?
5. How can this concept be applied to different geometric problems involving composite figures?

Tip: In problems involving composite figures, break down the problem into smaller parts, such as analyzing each shape's dimensions individually before applying formulas.