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, equal to _________.
A. 1/4
B. 1/8
C. 1/16
D. 1/2
GATE 2021 · General Aptitude · Paper Folding · medium
Answer: The area of each face of the final folded shape is 1/8 sq unit. Answer: B.
Initial area: The square sheet has side 1 unit, so its initial area is 1 sq unit.
Fold 1: along the main diagonal: Folding along the main diagonal of a square halves the face area. The resulting shape is a right-angled isosceles triangle. Area = 1/2 sq unit.
Fold 2: along the line of symmetry of the triangle: The right isosceles triangle is folded along its altitude from the right-angle vertex (its line of symmetry), producing a smaller right isosceles triangle. Area = 1/4 sq unit.
Fold 3: along the line of symmetry of the current shape: Folding again along the line of symmetry of the triangle halves the face area once more. Final face area = 1/8 sq unit.