Calculate Trapezoid Perimeters: Comparing Two Shapes with 7-Unit Parallel Sides

To find the solution, we begin by calculating the perimeters of each trapezoid:

For trapezoid $A$, the sides are $4$, $7$, $7$, and $5$. Therefore, the perimeter $pA$ is:

$pA = 4 + 7 + 7 + 5 = 23$

For trapezoid $B$, the sides are $2$, $7$, $11$, and $3$. Thus, the perimeter $pB$ is:

$pB = 2 + 7 + 11 + 3 = 23$

Both trapezoids have identical perimeters of $23$. However, their areas cannot be determined to be identical without information about the heights of the trapezoids. Since these are crucial for the area calculation, the equivalence of their areas cannot be concluded from available data.

Therefore, the perimeter is $pA = pB = 23$, but their areas are not necessarily identical.