Calculate Rectangle Perimeter with Congruent Triangles: 6x8 Geometric Figure

To solve this problem, we'll follow these steps:

• Step 1: Analyze the congruent triangles.

• Step 2: Use congruence to identify side lengths.

• Step 3: Calculate the perimeter of the rectangle.

Now, let's work through each step:
Step 1: The problem states that $\triangle AED \cong \triangle BCD$, which means corresponding sides and angles are equal.
Step 2: Identify corresponding sides from congruence:
- $AE = CD = 6$ because corresponding sides of congruent triangles are equal.
- $AD = BC$. Since $AB = 8$ and using the fact $\triangle AED$ and $\triangle BCD$ are congruent, $BD$ (the same as $AD$) must also equal 6 (from the congruence starting from point $D$).
- Thus, $AD = 6$.

Step 3: Calculate the perimeter: $AF = DE = 6$ from congruency and $AD = FE = 6$. Since both pairs of opposite sides of the rectangle are equal, the rectangle perimeter is:
$P = 2(AF + AD) = 2(6 + 8) = 2 \times 14 = 28$

Therefore, the perimeter of the rectangle $AFDE$ is $28$.