Question 1209964
Okay, let's break down this problem step-by-step.

**1. Area of the Right Triangle ABC:**

* Since ABC is a right triangle with AB = 4 cm and BC = 4 cm, we can use the formula for the area of a triangle:
    * Area = (1/2) * base * height
    * Area(ABC) = (1/2) * 4 cm * 4 cm = 8 cm²

**2. Area of the Parallelogram ACDF:**

* We know that AF = 20 cm.
* Since ACDF is a parallelogram, CD = AF = 20 cm.
* To find the area of the parallelogram, we need the base and the height.
* Since the height of the parrallelogram is the same as the length of AB and BC, the height is 4cm.
* Area(ACDF) = base * height
    * Area(ACDF) = 20 cm * 4 cm = 80 cm²

**3. Area of the Sector DEF:**

* We are given that angle EDF = 35 degrees.
* We need to find the radius of the sector. Since ACDF is a parallelogram, CD = AF. Also, since ABC is a right triangle with AB = BC, then the length of AC = sqrt(4^2 + 4^2) = sqrt(16+16) = sqrt(32) = 4 * sqrt(2). Because ACDF is a parallelogram, then DE = AC = 4 * sqrt(2) cm. This is the radius of the sector.
* The area of a sector is given by:
    * Area = (θ/360°) * π * r²
    * Area(DEF) = (35°/360°) * π * (4√2 cm)²
    * Area(DEF) = (35/360) * π * 32 cm²
    * Area(DEF) = (7/72) * 32π cm²
    * Area(DEF) = (224/72)π cm²
    * Area(DEF) = (28/9)π cm²
    * Area(DEF) ≈ 9.77π cm²
    * Area(DEF) ≈ 30.7 cm²

**4. Total Area of the Composite Figure:**

* Total Area = Area(ABC) + Area(ACDF) + Area(DEF)
* Total Area = 8 cm² + 80 cm² + (28/9)π cm²
* Total Area = 88 cm² + (28/9)π cm²
* Total Area ≈ 88 cm² + 30.7 cm²
* Total Area ≈ 118.7 cm²

**Therefore, the total area of the composite figure is approximately 118.7 cm².**