To determine the area of the design in square inches, we break the figure into two distinct parts:

1. The rectangular section of the design.
2. The semicircular section at the top.

Step 1: Convert all dimensions to inches

• The rectangle has dimensions:
  • Height: $9 \, \text{inches}$
  • Width: $1.5 \, \text{feet} = 1.5 \times 12 = 18 \, \text{inches}$

Step 2: Area of the rectangular section

The area of a rectangle is given by: $\text{Area}_{\text{rectangle}} = \text{Height} \times \text{Width}$ $\text{Area}_{\text{rectangle}} = 9 \, \text{inches} \times 18 \, \text{inches} = 162 \, \text{square inches}$

Step 3: Area of the semicircular section

The radius of the semicircle is half of the width of the rectangle: $\text{Radius} = \frac{18}{2} = 9 \, \text{inches}$

The area of a circle is: $\text{Area}_{\text{circle}} = \pi r^2$ For a semicircle: $\text{Area}_{\text{semicircle}} = \frac{1}{2} \pi r^2$ Substitute $r = 9 \, \text{inches}$ and $\pi = 3.14$: $\text{Area}_{\text{semicircle}} = \frac{1}{2} \times 3.14 \times (9)^2$ $\text{Area}_{\text{semicircle}} = \frac{1}{2} \times 3.14 \times 81 = \frac{1}{2} \times 254.34 = 127.17 \, \text{square inches}$

Step 4: Total area of the design

The total area is the sum of the areas of the rectangle and the semicircle: $\text{Total Area} = \text{Area}_{\text{rectangle}} + \text{Area}_{\text{semicircle}}$ $\text{Total Area} = 162 + 127.17 = 289.17 \, \text{square inches}$

Final Answer:

The area of the design is approximately 289.17 square inches.

Do you want a detailed explanation for a particular step? Here are some related questions for further exploration:

1. How do you convert feet to inches in area problems?
2. What formula would you use if the semicircular design were instead a quarter circle?
3. Why is it important to use consistent units in area calculations?
4. How would the area change if the dimensions of the blanket were doubled?
5. What is the practical importance of using π approximations in real-world problems?

Tip: Always double-check unit conversions to ensure your calculations remain accurate!