To solve problems involving a combination of a rectangle and a semicircle, follow these general steps (assuming the semicircle is attached to one side of the rectangle):

Step 1: Identify Key Dimensions

Let the rectangle have:

• Length = ( L ) (e.g., horizontal side)
• Width = ( W ) (e.g., vertical side)

Assume the semicircle is attached to the length ( L ) (so its diameter = ( L ), radius ( r = L/2 )).

Step 2: Calculate Total Area

Total Area = Area of Rectangle + Area of Semicircle

• Area of Rectangle: ( A_{\text{rect}} = L \times W )
• Area of Semicircle: ( A_{\text{semi}} = \frac{1}{2} \times \pi r^2 = \frac{1}{2} \times \pi \times \left(\frac{L}{2}\right)^2 = \frac{\pi L^2}{8} )

Total Area: ( A_{\text{total}} = LW + \frac{\pi L^2}{8} )

Step 3: Calculate Perimeter

Perimeter = Sum of outer edges (exclude the attached side of the rectangle):

• Rectangle contributes: ( W + L + W = L + 2W ) (left, bottom, right sides)
• Semicircle contributes: Curved edge = ( \frac{1}{2} \times 2\pi r = \pi \times \frac{L}{2} = \frac{\pi L}{2} )

Total Perimeter: ( P_{\text{total}} = L + 2W + \frac{\pi L}{2} )

Example (if dimensions are given)

Suppose ( L = 10\,\text{cm} ), ( W = 6\,\text{cm} ):

• Area: ( (10×6) + \frac{\pi×10^2}{8} = 60 + 12.5\pi ≈ 99.27\,\text{cm}^2 )
• Perimeter: (10 + (2×6) + \frac{\pi×10}{2} = 22 +5\pi ≈37.7\,\text{cm} )

Note: Adjust the steps if the semicircle is attached to the width (( W )) instead of length (( L ))—swap ( L ) and ( W ) in the semicircle terms.

If you provide the exact dimensions from your image, I can give a precise answer!
Let me know the values, and I’ll compute it for you.

作者声明:本文包含人工智能生成内容。