Let’s solve the problem!

We are asked to find the approximate area of the red section of the semicircular window. Here's the breakdown:

Step 1: Calculate the radius of the semicircle

The diameter of the semicircle is given as $18$ inches.
Thus, the radius is: $r = \frac{18}{2} = 9 \text{ inches}.$

Step 2: Total area of the semicircle

The area of a full circle is: $A_{\text{circle}} = \pi r^2.$ For a semicircle, the area is half of this: $A_{\text{semicircle}} = \frac{1}{2} \pi r^2 = \frac{1}{2} \pi (9)^2 = \frac{1}{2} \pi (81) = 40.5 \pi \approx 127.234 \, \text{square inches}.$

Step 3: Proportion of the red section

The total angle in the semicircle is $180^\circ$. The red section spans $100^\circ$ (computed as $180^\circ - 40^\circ - 40^\circ$).
Thus, the proportion of the semicircle that is red is: $\text{Proportion (red)} = \frac{100}{180} = \frac{5}{9}.$

Step 4: Area of the red section

The area of the red section is: $A_{\text{red}} = \text{Proportion (red)} \times A_{\text{semicircle}} = \frac{5}{9} \times 127.234 \approx 70.7 \, \text{square inches}.$

Final Answer:

The red section of the window is approximately 70.7 square inches.
Thus, the correct choice is D.

Would you like further details or have any questions? 😊

Related Questions:

1. How do you compute the area of a quarter-circle window?
2. What would the area be if the semicircle had a radius of 12 inches?
3. How can you find the area of the green sections?
4. What is the total angle of the colored sections relative to the full circle?
5. What formula would you use if the window were elliptical?

Tip:

Always start by finding the radius when dealing with circle-related problems!