To solve for the area of the composite figure, let's break it into parts:

Step 1: Identify the components

The figure consists of:

1. A rectangle with dimensions:
   • Length = 15 ft
   • Height = 6 ft
2. A semi-circle (half of a circle) with:
   • Diameter = 6 ft → Radius $r = \frac{6}{2} = 3$ ft

The total area will be the sum of the rectangle's area and the semi-circle's area.

Step 2: Calculate the area of the rectangle

The formula for the area of a rectangle is: $A_{\text{rectangle}} = \text{Length} \times \text{Width}$ Substitute the values: $A_{\text{rectangle}} = 15 \times 6 = 90 \, \text{ft}^2$

Step 3: Calculate the area of the semi-circle

The formula for the area of a full circle is: $A_{\text{circle}} = \pi r^2$ Since the semi-circle is half of a circle: $A_{\text{semi-circle}} = \frac{1}{2} \pi r^2$ Using $\pi = 3.14$ and $r = 3$: $A_{\text{semi-circle}} = \frac{1}{2} \times 3.14 \times 3^2$ Simplify: $A_{\text{semi-circle}} = \frac{1}{2} \times 3.14 \times 9 = \frac{28.26}{2} = 14.13 \, \text{ft}^2$

Step 4: Add the areas

Now, add the areas of the rectangle and the semi-circle: $A_{\text{total}} = A_{\text{rectangle}} + A_{\text{semi-circle}}$ $A_{\text{total}} = 90 + 14.13 = 104.13 \, \text{ft}^2$

Final Answer:

The area of the composite figure is: $\boxed{104.13 \, \text{ft}^2}$

Let me know if you want further clarifications or a step-by-step breakdown of any part!

Related Questions:

1. How do you calculate the perimeter of this composite figure?
2. How would the area change if the rectangle’s dimensions were doubled?
3. What is the area of a full circle with a radius of 3 ft?
4. How do you find the area of a composite figure with more parts, such as triangles or trapezoids?
5. If the radius of the semi-circle were increased to 5 ft, how would the total area change?

Tip: Always divide complex figures into basic shapes (like rectangles, triangles, and circles) to simplify area calculations.