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The problem involves two triangles, \( QRS \) and \( WXY \), where triangle \( TUV \) is also part of the construction. Let's break down the steps to solve the problem:

### Given:
- Triangle \( QRS \) is an equilateral triangle with an area of 80 square inches.
- \( TUV \) is formed by joining the midpoints of the sides of \( QRS \).
- \( WXY \) is formed by joining the midpoints of the sides of \( TUV \).
- We need to find the area of triangle \( WXY \).

### Step-by-Step Solution:

1. **Midpoint Triangle Properties**:
   - When a triangle is formed by joining the midpoints of the sides of an equilateral triangle, the resulting triangle is also equilateral.
   - The area of the triangle formed by the midpoints is \( \frac{1}{4} \) of the area of the original triangle.

2. **Area of Triangle \( TUV \)**:
   - Since \( TUV \) is formed by joining the midpoints of triangle \( QRS \), the area of \( TUV \) is \( \frac{1}{4} \) of the area of \( QRS \).
   \[
   \text{Area of } TUV = \frac{1}{4} \times 80 = 20 \text{ square inches}.
   \]

3. **Area of Triangle \( WXY \)**:
   - Similarly, triangle \( WXY \) is formed by joining the midpoints of the sides of triangle \( TUV \), so the area of \( WXY \) is \( \frac{1}{4} \) of the area of \( TUV \).
   \[
   \text{Area of } WXY = \frac{1}{4} \times 20 = 5 \text{ square inches}.
   \]

Thus, the area of triangle \( WXY \) is **5 square inches**, which corresponds to option **A**.

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Would you like further details or have any questions?  
Here are five related questions that could extend your understanding:

1. What is the ratio of the areas of two similar triangles?
2. How does the perimeter of \( WXY \) compare to the perimeter of \( QRS \)?
3. How would the problem change if triangle \( QRS \) were not equilateral?
4. How can you generalize this problem to any triangle, not just equilateral ones?
5. What would be the side lengths of triangle \( WXY \) if the side length of triangle \( QRS \) were given?

**Tip**: When a triangle is divided by midpoints, the area of the new smaller triangle is always one-quarter of the original triangle, regardless of the type of triangle.

In the figure shown, triangle TUV is formed by joining the midpoints of the sides of equilateral triangle QRS. Triangle WXY is formed by joining the midpoints of the sides of triangle TUV. If the area of triangle QRS is 80 square inches, what is the area of triangle WXY?

Learn how to find the area of triangle WXY formed by the midpoints of triangle TUV, where TUV is also formed by the midpoints of an equilateral triangle QRS with an area of 80 square inches. This solution involves geometric properties and area ratios. Suitable for Grades 9-10.

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