To solve the given question, let's understand the areas of a parallelogram and a rectangle with the same side lengths, [tex]\(a\)[/tex] and [tex]\(b\)[/tex].
1. Area of a Rectangle:
- For a rectangle, the formula for the area is straightforward:
[tex]\[
B = a \times b
\][/tex]
where [tex]\(a\)[/tex] and [tex]\(b\)[/tex] are the lengths of the sides of the rectangle.
2. Area of a Parallelogram:
- For a parallelogram, the formula for the area depends on the base and the height (the perpendicular distance between the bases). If we consider [tex]\(a\)[/tex] as the base and [tex]\(h\)[/tex] as the height, the area [tex]\(A\)[/tex] is expressed as:
[tex]\[
A = a \times h
\][/tex]
- Note that the height [tex]\(h\)[/tex] will generally be less than or equal to the side length [tex]\(b\)[/tex] of the parallelogram because the height is the perpendicular dropped from the opposite vertex to the base [tex]\(a\)[/tex], and it doesn't exceed the slant height [tex]\(b\)[/tex].
3. Comparison of Areas:
- From the above understanding:
[tex]\[
A = a \times h \quad \text{and} \quad B = a \times b
\][/tex]
- Since the height [tex]\(h\)[/tex] is always less than or equal to the side length [tex]\(b\)[/tex], i.e., [tex]\(h \leq b\)[/tex], it follows:
[tex]\[
a \times h \leq a \times b
\][/tex]
which means:
[tex]\[
A \leq B
\][/tex]
Given the options:
1. [tex]\(A > B\)[/tex]
2. [tex]\(A = B\)[/tex]
3. [tex]\(A < B\)[/tex]
4. [tex]\(A \geq B\)[/tex]
Given the inequality [tex]\(A \leq B\)[/tex], the correct choice is:
[tex]\[
A \geq B
\][/tex]
Thus, the answer is:
[tex]\[
\boxed{4}
\][/tex]
