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To solve this problem, let's determine the maximum and minimum area of the triangle formed when the lower right corner of the rectangular paper is folded to the top edge.

### Steps to Determine Maximum and Minimum Areas:

#### 1. Analyze the Geometry
- The dimensions of the rectangle are \(x = 22.4 \, \text{cm}\) and \(y = 20 \, \text{cm}\).
- When the lower right corner is folded, a right triangle is formed with one vertex at the fold point on the top edge of the rectangle, another vertex at the bottom right corner of the rectangle, and the third vertex at the top right corner of the rectangle.

#### 2. Express the Area of the Triangle
The area of a triangle is given by:
\[
A = \frac{1}{2} \times \text{base} \times \text{height}
\]
In this case:
- The base of the triangle is the horizontal distance from the fold point to the right side of the rectangle.
- The height is the vertical distance from the fold point to the bottom side of the rectangle.

We need to determine how the base and height vary as the fold point moves along the top edge of the rectangle.

#### 3. Determine Maximum and Minimum Areas
To find the maximum and minimum areas:
1. Formulate the area as a function of the folding point.
2. Use calculus to find the critical points of the function.
3. Evaluate the area at the critical points and at the endpoints of the folding range (e.g., fold points at the left and right edges).

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### Let's Compute This
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You are given a rectangular piece of paper that has length x = 22.4 cm and height y = 20 cm. The lower right corner is to be folded to the top edge forming a triangle as shown. Determine the maximum and minimum area of a triangle that can be constructed.

Find the maximum and minimum area of a triangle formed by folding a rectangular piece of paper (length 22.4 cm, height 20 cm). This geometry problem involves optimization principles, area formulas, and critical point analysis, suitable for Grades 10-12.

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