Question

Consider a square sheet of side 1 unit. The sheet is first folded along the main diagonal. This is followed by a fold along its line of symmetry. The resulting folded shape is again folded along its line of symmetry. The area of each face of the final folded shape, in square units, is equal to \(\underline{\hspace{2cm}}\)

• A. \( \frac{1}{4} \)
• B. \( \frac{1}{8} \)
• C. \( \frac{1}{16} \)
• D. \( \frac{1}{32} \)

Hint:

When folding a shape along its symmetry lines, each fold typically halves the area. For multiple folds, the area of each face is reduced exponentially.

Answer 1

The Correct Option is B

We are given a square sheet with a side length of 1 unit. The problem involves multiple folds along the symmetry lines. Let's analyze this step by step:
1. First Fold: The sheet is folded along the main diagonal, which divides the square into two equal right-angled triangles. The area of each triangle is: \[ \text{Area of each triangle} = \frac{1}{2} \, \text{(since area of the square is 1 unit)}. \] 2. Second Fold: The resulting folded shape is folded along its line of symmetry (which is now a rectangle). The area of each face of the folded shape after the second fold is halved again. So, each face now has an area of: \[ \frac{1}{2} \times \frac{1}{2} = \frac{1}{4}. \] 3. Third Fold: Finally, the folded shape is folded again along its line of symmetry, cutting the area of each face in half once again. After this final fold, the area of each face becomes: \[ \frac{1}{2} \times \frac{1}{4} = \frac{1}{8}. \] Thus, the area of each face of the final folded shape is \( \frac{1}{8} \) square units. Therefore, the correct answer is (B).