The diagram you provided shows a shape that consists of a rectangle with a semicircular top. The dimensions provided are 20 yards for the width and 936 inches for the height of the semicircular part. To find the perimeter and area of this figure, we need to convert all measurements to the same unit and then calculate each part.

Step 1: Convert Measurements

First, we'll convert the height from inches to yards (since 1 yard = 36 inches).

• Height in yards: $\frac{936}{36} = 26$ yards

The total height of the rectangle including the semicircle is 26 yards. Assuming the total height includes the rectangle, let's deduce the rectangle's height:

• Height of rectangle: $\text{Total height} - \text{radius of semicircle}$
• Radius of semicircle = $\frac{26}{2} = 13$ yards
• Height of rectangle = $26 - 13 = 13$ yards

Step 2: Calculate Perimeter

The perimeter of the shape (P) is the sum of the widths and heights of the rectangle plus the circumference of the semicircle:

• Perimeter of the rectangle: $2 \times \text{width} + 2 \times \text{height of rectangle} = 2 \times 20 + 2 \times 13 = 40 + 26 = 66$ yards
• Circumference of the full circle: $2 \pi r = 2 \pi \times 13 = 26 \pi$
• Perimeter of the semicircle: $\frac{26 \pi}{2} = 13 \pi$ yards
• Total perimeter: $66 + 13 \pi$ yards (about $66 + 40.84 = 106.84$ yards)

Step 3: Calculate Area

The area of the shape (A) is the sum of the area of the rectangle and the area of the semicircle:

• Area of the rectangle: $\text{width} \times \text{height of rectangle} = 20 \times 13 = 260$ square yards
• Area of the full circle: $\pi r^2 = \pi \times 13^2 = 169 \pi$
• Area of the semicircle: $\frac{169 \pi}{2} \approx 84.5 \pi$ square yards
• Total area: $260 + 84.5 \pi$ square yards (about $260 + 265.48 = 525.48$ square yards)

Conclusion

• Perimeter: Approximately 106.84 yards
• Area: Approximately 525.48 square yards

Would you like more detail on any of these steps or have any questions? Here are some related questions you might find helpful:

1. How would the perimeter and area change if the semicircle was replaced with a quarter circle?
2. What is the impact of changing the width of the rectangle on both the perimeter and the area?
3. How does the area of a semicircle compare to the area of the full circle for the same radius?
4. What is the formula for the circumference of a circle and why is it important?
5. How can the concepts of perimeter and area be applied in real-life situations?

Tip: Always ensure units are consistent across all dimensions when calculating area or perimeter to avoid errors in your final results.