To determine the area of the large rectangle, we need to extract and analyze the information provided in the image.

1. The large rectangle is divided into five smaller congruent rectangles.
2. The short side of the shaded rectangle has length 2.

Since the large rectangle is divided into five congruent rectangles, we can infer the following:

• The shaded rectangle is congruent to each of the other four smaller rectangles.
• The shaded rectangle and each of the other rectangles share the same dimensions.

Step-by-Step Solution

1. Dimensions of the Smaller Rectangles:

   • Each of the five smaller rectangles has the same dimensions.
   • Let the dimensions of each smaller rectangle be $w$ (width) and $h$ (height).

2. Short Side of the Shaded Rectangle:

   • The short side of the shaded rectangle (which is $w$) is given as 2.
   • Therefore, $w = 2$.

3. Dividing the Large Rectangle:

   • Since the large rectangle is divided into 5 smaller rectangles, and it is given that the smaller rectangles are placed side by side along the height of the large rectangle, the height of the large rectangle can be expressed as $5h$.

4. Calculating the Area of the Large Rectangle:

   • The area $A$ of the large rectangle is given by its width multiplied by its height: $A = \text{width} \times \text{height}$
   • Here, the width is $w = 2$ and the height is $5h$.

Finding $h$:

To determine $h$, we observe the congruent nature of the rectangles:

• If the large rectangle is cut into 5 smaller congruent rectangles, then each rectangle's height must be $\frac{1}{5}$ of the large rectangle's total height.

Since there is no specific height given, and only the short side of the shaded rectangle is mentioned as 2, we deduce:

• The height $h$ of each smaller rectangle must align proportionally with the large rectangle.

Calculating the Total Height:

• Given the large rectangle's height must be $5h$, and each smaller rectangle has height $h$, we use:

$\text{Height of each smaller rectangle} = h$

If no specific additional height information is given, we use the information:

• Assuming standard dimensions, if each smaller rectangle height $h$ aligns with width $w$:

Therefore,

• For this specific case, the large rectangle’s total area involves: $A = w \times 5w = 2 \times 5 \times 2 = 2 \times 10 = 20$

The area of the large rectangle is 20 square units.

Would you like further details or have any questions? Here are some related questions:

1. What is the perimeter of the large rectangle?
2. How would the area change if the short side of the shaded rectangle was 3?
3. Can you calculate the area if the large rectangle was divided into 6 congruent rectangles?
4. What would be the dimensions of the large rectangle if each smaller rectangle had width 3?
5. How do you find the area of a rectangle when only given the length and perimeter?
6. What would be the area of one of the smaller rectangles?
7. How do you calculate the diagonal length of the large rectangle?
8. What are the properties of congruent rectangles in terms of area and perimeter?

Tip: When dealing with geometric shapes, always consider congruence and proportionality to solve for unknown dimensions.