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4. Shade the rectangle to break it into two smaller rectangles. Then complete the equations to find the total area of the large rectangle. Each \( \square \) represents 1 square unit.

Ask by Schultz Hall. in the United States
Mar 13,2025

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Answer

To find the total area of the large rectangle, divide it into two smaller rectangles, calculate each smaller area, and then add them together.

Solution

To solve the problem of finding the total area of a large rectangle that has been divided into two smaller rectangles, we can follow these steps: 1. **Identify the dimensions of the large rectangle**: Let's denote the length of the large rectangle as \( L \) and the width as \( W \). 2. **Calculate the area of the large rectangle**: The area \( A \) of a rectangle is calculated using the formula: \[ A = L \times W \] 3. **Break the rectangle into two smaller rectangles**: If the rectangle is divided, we can denote the dimensions of the two smaller rectangles. Let's say the first smaller rectangle has dimensions \( L_1 \) and \( W_1 \), and the second smaller rectangle has dimensions \( L_2 \) and \( W_2 \). 4. **Set up the equations**: The total area of the large rectangle can also be expressed as the sum of the areas of the two smaller rectangles: \[ A = A_1 + A_2 \] where \( A_1 = L_1 \times W_1 \) and \( A_2 = L_2 \times W_2 \). 5. **Complete the equations**: We can express the total area as: \[ A = (L_1 \times W_1) + (L_2 \times W_2) \] Now, if you provide the specific dimensions or any additional information about the rectangles, I can help you calculate the total area more precisely.

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To shade the rectangle and break it into two smaller rectangles, you could draw a vertical or horizontal line across the rectangle. For instance, if you draw a vertical line, you can separate the larger rectangle into two smaller rectangles, each having a defined base and height. To find the total area of the large rectangle, you can add up the areas of the two smaller rectangles. If rectangle A has a length of \( l_1 \) and a width of \( w_1 \), its area would be \( A_1 = l_1 \times w_1 \). For rectangle B, with dimensions \( l_2 \) and \( w_2 \), its area would be \( A_2 = l_2 \times w_2 \). The total area is then calculated as \( A_{\text{total}} = A_1 + A_2 = (l_1 \times w_1) + (l_2 \times w_2) \). Voilà! Total area achieved!

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