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

To find the area of rectangle ABCD, we can use the formula for the area of a rectangle: \( \text{Area} = \text{length} \times \text{width} \). If we let the length be represented by \( AB \) and the width by \( AD \), the area can be expressed as \( \text{Area} = AB \times AD \). Since opposite sides of a rectangle are equal, \( AB = CD \) and \( AD = BC \), confirming the rectangle's properties help reinforce this calculation visually and practically. In parallelogram XEFC, it's interesting to note that its area can also be calculated using the same concept of base and height – \( \text{Area} = \text{base} \times \text{height} \). Therefore, if you know the dimensions of parallelogram XEFC, you can compare those values with rectangle ABCD's area calculations, leading to fun insights about how different shapes relate to each other in terms of area!