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To solve the problem of calculating the area of the figure composed of a rectangle and a semicircle, follow these steps:

Step 1: Identify the given values

• Rectangle: length = 10 cm, width = 6 cm
• Semicircle: diameter = width of rectangle = 6 cm → radius (r = 6/2 = 3) cm

Step 2: Calculate the area of the rectangle

Area of rectangle = length × width
[A_{\text{rectangle}} = 10 \times 6 = 60\ \text{cm}^2]

Step 3: Calculate the area of the semicircle

Area of semicircle = (\frac{1}{2} \pi r^2)
Using (\pi ≈ 3.14):
[A_{\text{semicircle}} = \frac{1}{2} \times 3.14 \times 3^2 = \frac{1}{2} \times 3.14 \times 9 = 14.13\ \text{cm}^2]

Step 4: Total area of the figure

Add the areas of the rectangle and the semicircle:
[A{\text{total}} = A{\text{rectangle}} + A_{\text{semicircle}} = 60 + 14.13 = 74.13\ \text{cm}^2]

Answer: (\boxed{74.13}) square centimeters. (Or (\boxed{60 + \frac{9\pi}{2}}) if leaving in terms of π.)

For practical purposes, the numerical value is (\boxed{74.13}).

(\boxed{74.13})

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