To solve problems involving a rectangle with attached semicircles, follow these general steps (common scenario: rectangle with two semicircles on opposite sides):

Step 1: Identify Key Dimensions

Let:

• ( l = \text{length of the rectangle (side not attached to semicircles)} )
• ( w = \text{width of the rectangle (diameter of each semicircle)} )
• ( r = \frac{w}{2} = \text{radius of each semicircle} )

Step 2: Calculate Perimeter

The perimeter excludes the rectangle sides where semicircles are attached. It consists of:

• 2 × length of the rectangle
• Circumference of one full circle (2 semicircles = 1 circle)

Formula:
[ \text{Perimeter} = 2l + \pi w ]

Step 3: Calculate Area

The area is the sum of:

• Area of the rectangle
• Area of one full circle (2 semicircles = 1 circle)

Formula:
[ \text{Area} = l \times w + \pi r^2 = lw + \pi \left(\frac{w}{2}\right)^2 ]

Example Application

If ( l = 10\,\text{cm} ) and ( w = 6\,\text{cm} ):

• Perimeter: ( 2×10 + π×6 = 20 + 6π ≈ 38.84\,\text{cm} )
• Area: ( 10×6 + π×(3)^2 = 60 +9π ≈88.26\,\text{cm}^2 )

Note: Adjust if semicircles are attached to longer sides (swap ( l ) and ( w ) in diameter terms). Use your specific dimensions from the image to compute the result!

Let me know if you share the exact numbers from the image, and I’ll help compute the final answer.

作者声明:本文包含人工智能生成内容。