Question

a geometric figure labeled with a circle containing 4, and dimensions: top side 4 cm, left vertical segment 2 cm, bottom side 4 cm, and a vertical arrow of 4 cm on the right. the figure has a rectangular top part with right angles and a parallelogram - like bottom part.

Explanation:

Step1: Split the figure into a rectangle and a parallelogram.

The rectangle has length \( 4 \, \text{cm} \) and width \( 2 \, \text{cm} \). The parallelogram has base \( 4 \, \text{cm} \) and height \( 4 \, \text{cm} \).

Step2: Calculate the area of the rectangle.

The area of a rectangle is given by \( A_{\text{rectangle}} = \text{length} \times \text{width} \). So, \( A_{\text{rectangle}} = 4 \times 2 = 8 \, \text{cm}^2 \).

Step3: Calculate the area of the parallelogram.

The area of a parallelogram is given by \( A_{\text{parallelogram}} = \text{base} \times \text{height} \). So, \( A_{\text{parallelogram}} = 4 \times 4 = 16 \, \text{cm}^2 \).

Step4: Sum the areas of the rectangle and the parallelogram.

Total area \( A = A_{\text{rectangle}} + A_{\text{parallelogram}} = 8 + 16 = 24 \, \text{cm}^2 \).

Answer:

The area of the figure is \( 24 \, \text{cm}^2 \).