To solve for the area of the figure in the image, let’s break it down into two main parts: the rectangular section and the half-circle section.

Step 1: Area of the Rectangle

The rectangle has dimensions:

• Length = $9$ yards
• Height = $8$ yards

The area of a rectangle is calculated by: $\text{Area of rectangle} = \text{length} \times \text{height} = 9 \times 8 = 72 \text{ square yards}$

Step 2: Area of the Half-Circle

The half-circle has a diameter equal to the height of the rectangle, which is $8$ yards. Therefore, the radius $r$ of the half-circle is: $r = \frac{8}{2} = 4 \text{ yards}$

The area of a full circle is given by $\pi r^2$. Since we have only half of a circle, we divide by 2: $\text{Area of half-circle} = \frac{1}{2} \pi r^2 = \frac{1}{2} \times 3.14 \times 4^2 = \frac{1}{2} \times 3.14 \times 16 = 25.12 \text{ square yards}$

Step 3: Total Area of the Figure

Adding the area of the rectangle and the area of the half-circle gives the total area: $\text{Total Area} = 72 + 25.12 = 97.12 \text{ square yards}$

Answer

The area enclosed by the figure is: $\boxed{97.12 \text{ square yards}}$

Would you like a further breakdown of any of these steps?

Related Questions

1. How would the area change if the diameter of the half-circle was different?
2. What would the area be if the shape included a full circle instead of a half-circle?
3. How is the area formula for circles derived from the radius?
4. How would the area change if the rectangle had different length or height values?
5. Can this figure’s area be calculated using integration?

Tip

When dealing with composite figures, break them down into simpler shapes (like rectangles, triangles, or circles) for easier calculations.