Figure Analysis Flashcards

The sequence of images shows a square piece of paper being folded, and then one or more holes are punched through it. Identify what the paper will look like when it is fully unfolded.

Answer: A square with four holes, one in the center of each quadrant.

The paper is first folded in half vertically, then folded in half again horizontally. This creates four layers. A single hole is punched through the center of this smaller, folded square. When unfolded, this single hole will be replicated in each of the four quadrants due to the folds. Therefore, the unfolded paper will have four holes, one in the center of each quadrant.

A square piece of paper is folded diagonally from the top right corner to the bottom left corner. Then, it is folded again along the new diagonal. A circular hole is punched through the top corner of the resulting triangle. Which of the following options represents the unfolded paper?

Answer: A square with two holes along the main diagonal from top right to bottom left.

The first diagonal fold creates two layers. The second diagonal fold creates four layers. Punching a hole in the corner of this final triangle goes through all four layers. Unfolding the second fold mirrors the hole across that fold line. Unfolding the first, main diagonal fold mirrors the two resulting holes across the main diagonal (top right to bottom left). This results in two holes along that diagonal line.

The images show a piece of paper being folded. The first fold is horizontal across the middle. The second fold is vertical across the middle. A straight cut is then made, removing the corner where all the free edges meet. What will the unfolded paper look like?

Answer: A large square with a smaller square hole in the center.

Folding the paper horizontally and then vertically concentrates the center of the original paper at one corner of the folded square. The cut removes the opposite corner, which contains the four original corners of the paper. When unfolded, the cut will be mirrored across the fold lines, creating a symmetrical square hole in the very center of the paper.

A rectangular piece of paper is folded in half lengthwise. A triangular hole is punched through the center of the folded edge. Which of the following best describes the appearance of the paper when unfolded?

Answer: A rectangle with a diamond-shaped (rhombus) hole in the middle.

The fold is along one of the long sides of the triangle being punched out. When the paper is unfolded, the triangular hole is mirrored across the fold line. A triangle mirrored against itself along one of its sides creates a diamond shape (a rhombus).

In a Figure Analysis scenario, a square paper is folded in half vertically. Then, a semi-circular hole is punched along the folded edge. What shape is the hole when the paper is unfolded?

Answer: A full circle.

The straight edge of the semi-circle is placed along the fold. When the paper is unfolded, this semi-circle is mirrored on the other side of the fold line. A semi-circle mirrored against its straight edge forms a complete circle.

A square piece of paper is folded three times. First, it is folded in half horizontally. Second, it is folded in half vertically. Third, it is folded diagonally. A small hole is punched through all layers near the center of the final triangle's longest side. How many holes will there be when the paper is fully unfolded?

Answer: 8 holes

The first horizontal fold creates 2 layers. The second vertical fold creates 4 layers. The third diagonal fold creates 8 layers. Since the hole is punched through all layers of the final folded shape, there will be 8 holes when the paper is fully unfolded.