The given shape is a rectangle with two semicircles attached on opposite ends. Let's calculate both the area and perimeter step by step:

Step 1: Understand the dimensions

• The rectangle's length = $6 \, \text{m}$
• The radius of the semicircles = $1.8 \, \text{m}$ (given as the width of one semicircle's diameter).
• The total length of the shape (including both semicircles) = $6 + 2 \times \text{radius} = 6 + 3.6 = 9.6 \, \text{m}$.

Step 2: Calculate the area

1. Area of the rectangle: $A_{\text{rectangle}} = \text{length} \times \text{width} = 6 \times 1.8 = 10.8 \, \text{m}^2$

2. Area of the two semicircles: The combined area of two semicircles is equal to the area of one full circle: $A_{\text{circle}} = \pi \times r^2 = \pi \times (1.8)^2 \approx 3.14 \times 3.24 \approx 10.18 \, \text{m}^2$

3. Total area: $A_{\text{total}} = A_{\text{rectangle}} + A_{\text{circle}} = 10.8 + 10.18 \approx 20.98 \, \text{m}^2$

Step 3: Calculate the perimeter

1. Perimeter of the rectangle (excluding the semicircles): The two straight sides are $2 \times \text{length} = 2 \times 6 = 12 \, \text{m}$.

2. Perimeter of the semicircles: The combined perimeter of two semicircles is equal to the circumference of one full circle: $P_{\text{circle}} = 2 \pi r = 2 \pi (1.8) \approx 2 \times 3.14 \times 1.8 \approx 11.30 \, \text{m}$

3. Total perimeter: $P_{\text{total}} = 12 + 11.30 = 23.30 \, \text{m}$

Final Answers

• Area: $20.98 \, \text{m}^2$ (approximately)
• Perimeter: $23.30 \, \text{m}$ (approximately)

Would you like further explanation or steps clarified? 😊

5 Related Questions

1. What is the formula for the area of a semicircle, and how does it differ from a full circle?
2. How do you calculate the perimeter of composite shapes like this one?
3. How can the accuracy of these calculations be improved (e.g., using more precise values for $\pi$)?
4. What would the area and perimeter be if the radius was doubled?
5. How does adding semicircles to a rectangle affect the perimeter compared to adding full circles?

Tip

For composite shapes, break them into simpler shapes (rectangles, circles, etc.) to compute their area and perimeter systematically.