[a] In the opposite figure : ABCD is a rectangle , XEFC is a parallelogram. Prove that : The area of the rectangle $$ \mathrm{ABCD}= $$ The

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To prove that the area of rectangle $$ABCD$$ is equal to the area of parallelogram $$XEFC$$, we can follow these steps:

1. **Identify the dimensions of the rectangle**:
   - Let the length of rectangle $$ABCD$$ be $$l$$ and the width be $$w$$.
   - The area of rectangle $$ABCD$$ can be calculated using the formula:
     $$
     A_{ABCD} = l \times w
     $$

2. **Identify the dimensions of the parallelogram**:
   - For parallelogram $$XEFC$$, let the base $$EF$$ be equal to the length $$l$$ of rectangle $$ABCD$$.
   - Let the height from point $$X$$ to line $$EF$$ be $$h$$.
   - The area of parallelogram $$XEFC$$ can be calculated using the formula:
     $$
     A_{XEFC} = \text{base} \times \text{height} = l \times h
     $$

3. **Relate the height of the parallelogram to the rectangle**:
   - If point $$X$$ is directly above line $$EF$$ and the height $$h$$ is equal to the width $$w$$ of rectangle $$ABCD$$, then we can substitute $$h$$ with $$w$$:
     $$
     A_{XEFC} = l \times w
     $$

4. **Conclusion**:
   - Since both areas are equal:
     $$
     A_{ABCD} = l \times w = A_{XEFC}
     $$
   - Therefore, we have proven that the area of rectangle $$ABCD$$ is equal to the area of parallelogram $$XEFC$$:
     $$
     A_{ABCD} = A_{XEFC}
     $$

This completes the proof.
The area of rectangle $$ABCD$$ is equal to the area of parallelogram $$XEFC$$.

[a] In the opposite figure : ABCD is a rectangle , XEFC is a parallelogram. Prove that : The area of the rectangle \( \mathrm{ABCD}= \) The

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