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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)1/8
- b)1/16
- c)1/4
- d)1/3
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
Consider a square sheet of side 1 unit. The sheet is first folded alon...
Given:
- A square sheet of side 1 unit
- The sheet is 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
To find:
- The area of each face of the final folded shape
Solution:
To solve this problem, let's follow the steps and visualize the folding process:
Step 1: Fold along the main diagonal
When we fold the square sheet along its main diagonal, the two opposite corners of the square come together and overlap. This creates a triangle with a base equal to the length of the square's side and a height equal to half the length of the square's side.
Step 2: Fold along the line of symmetry
Next, we fold the resulting shape along its line of symmetry. This line of symmetry is the perpendicular bisector of the diagonal. As a result, the triangle formed in step 1 is folded in half along its height, creating a smaller triangle.
Step 3: Fold along the line of symmetry again
Finally, we fold the resulting shape along its line of symmetry one more time. This line of symmetry is the bisector of the remaining side of the triangle. As a result, the smaller triangle formed in step 2 is folded in half along its height again, creating an even smaller triangle.
Calculating the area of each face
Now, let's calculate the area of each face of the final folded shape.
- The original square sheet has an area of 1 unit².
- After folding along the main diagonal, the resulting triangle has an area of (1/2) * (1/2) = 1/4 unit².
- After folding along the line of symmetry, the resulting smaller triangle has half the area of the previous triangle, which is (1/4) * (1/2) = 1/8 unit².
- After folding along the line of symmetry again, the resulting even smaller triangle has half the area of the previous triangle, which is (1/8) * (1/2) = 1/16 unit².
Therefore, the area of each face of the final folded shape is 1/16 unit². So, the correct answer is option D.
- A square sheet of side 1 unit
- The sheet is 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
To find:
- The area of each face of the final folded shape
Solution:
To solve this problem, let's follow the steps and visualize the folding process:
Step 1: Fold along the main diagonal
When we fold the square sheet along its main diagonal, the two opposite corners of the square come together and overlap. This creates a triangle with a base equal to the length of the square's side and a height equal to half the length of the square's side.
Step 2: Fold along the line of symmetry
Next, we fold the resulting shape along its line of symmetry. This line of symmetry is the perpendicular bisector of the diagonal. As a result, the triangle formed in step 1 is folded in half along its height, creating a smaller triangle.
Step 3: Fold along the line of symmetry again
Finally, we fold the resulting shape along its line of symmetry one more time. This line of symmetry is the bisector of the remaining side of the triangle. As a result, the smaller triangle formed in step 2 is folded in half along its height again, creating an even smaller triangle.
Calculating the area of each face
Now, let's calculate the area of each face of the final folded shape.
- The original square sheet has an area of 1 unit².
- After folding along the main diagonal, the resulting triangle has an area of (1/2) * (1/2) = 1/4 unit².
- After folding along the line of symmetry, the resulting smaller triangle has half the area of the previous triangle, which is (1/4) * (1/2) = 1/8 unit².
- After folding along the line of symmetry again, the resulting even smaller triangle has half the area of the previous triangle, which is (1/8) * (1/2) = 1/16 unit².
Therefore, the area of each face of the final folded shape is 1/16 unit². So, the correct answer is option D.
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Community Answer
Consider a square sheet of side 1 unit. The sheet is first folded alon...
Area of ΔAOB = 1/2BO × OA
= 1/2 x 1/2 x 1/2 = 1/8 Sqaure Unit
Hence, the correct option is (D).
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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)1/8 b)1/16 c)1/4 d)1/3Correct answer is option 'D'. Can you explain this answer?
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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)1/8 b)1/16 c)1/4 d)1/3Correct answer is option 'D'. Can you explain this answer? for Mechanical Engineering 2025 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about 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)1/8 b)1/16 c)1/4 d)1/3Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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)1/8 b)1/16 c)1/4 d)1/3Correct answer is option 'D'. Can you explain this answer?.
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)1/8 b)1/16 c)1/4 d)1/3Correct answer is option 'D'. Can you explain this answer? for Mechanical Engineering 2025 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about 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)1/8 b)1/16 c)1/4 d)1/3Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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)1/8 b)1/16 c)1/4 d)1/3Correct answer is option 'D'. Can you explain this answer?.
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