请解答---Here is the extracted content from the image: **Title:** 3. 不规则图形 (Irregular Shapes) (建议用时: 25分钟) (Suggested time: 25 minutes) **Header:** 班级: ______ 姓名: ______ (Class: ____ Name: ____) **Section Header:** 一、选择。(10分) (Part 1: Multiple Choice. (10 points)) **Question 1:** 1. (西城区)在一张边长是6厘米的正方形纸中, 剪去一个长4厘米、宽2厘米的长方形。京小圈想到三种方法, 剪完后剩下的部分如下图。比较下面三个图形的周长和面积, 说法正确的是( )。(单位: 厘米) **(Translation):** 1. (Xicheng District) From a square piece of paper with a side length of 6 cm, a rectangle with a length of 4 cm and a width of 2 cm is cut out. Jing Xiaoquan thought of three ways, and the remaining parts after cutting are shown in the figures below. Compare the perimeter and area of the following three figures, the correct statement is ( ). (Unit: cm) **Chart Description (for Question 1):** Type: Three geometric figures (likely the remaining parts after cutting). Main Elements: * Figure 1 (Left): A shaded L-shaped figure. Dimensions are labeled on the edges. Top edge length: 6. Right edge length: 6. A cut-out rectangle is implied, creating an inner corner. The visible external dimensions are 6 (left) and 6 (bottom). Internal dimensions are implied by the cut-out of 4x2. The shape can be seen as a 6x6 square with a 4x2 rectangle removed from a corner. The remaining shape has external dimensions 6x6. The internal corner sides have lengths 6-4=2 and 6-2=4. Dimensions explicitly labeled: 4, 6 (vertical on right), 6 (horizontal on bottom). * Figure 2 (Middle): A shaded U-shaped figure. Dimensions are labeled on the edges. Total width at the bottom is 6. Two vertical segments rise from the bottom edge. There's a gap between the vertical segments. Dimensions explicitly labeled: 4 (height of vertical segments), 2 (width of the gap), 6 (total width at the bottom). The vertical segments have a width of (6-2)/2 = 2 each. Total height is 4 + some part. Looking closely, the vertical segments seem to extend to a height of 4. The bottom horizontal segment is 6. The two vertical segments are 4 high and 2 wide. The connecting horizontal segment at the top is 2 long. * Figure 3 (Right): A shaded irregular figure, resembling a step or two connected rectangles. Dimensions are labeled on the edges. The overall shape is within a 6x6 area. Dimensions explicitly labeled: 4 (height of the left part), 6 (total width at the bottom), 6 (total height on the right), 2 (width of the right part). This shape appears to be formed by a 4x6 rectangle and a 2x2 square stacked on top of the right side. Or, a 6x6 square with a 4x4 rectangle removed from the top left. The remaining shape has a 6x6 outer boundary. The explicit labels suggest: Bottom horizontal 6, right vertical 6. An internal corner suggests a cut. A vertical segment of length 4 is on the left. A horizontal segment of length 4 is at height 4 from the bottom. A vertical segment of length 2 is on the right, from height 4 to 6. A horizontal segment of length 2 is at height 6, connecting to the top right corner. This interpretation is not consistent with the labels. Let's re-examine the labels. Figure 1: 4 (internal horizontal cut edge), 6 (external right edge), 6 (external bottom edge), 2 (internal vertical cut edge). Figure 2: 4 (vertical height of arms), 2 (width of gap), 6 (external bottom edge), 2 (internal top edge). Figure 3: 4 (horizontal segment at height 4), 6 (external bottom edge), 6 (external right edge), 2 (vertical segment at height 4-6 on right), 2 (horizontal segment at height 6 on top). Let's assume the original square was 6x6. The cut rectangle is 4x2. Area removed is 4 * 2 = 8. Original area is 6 * 6 = 36. Remaining area is 36 - 8 = 28 for all three figures. So, the areas of the three figures are equal. Let's calculate the perimeters. Figure 1: Starts as 6x6 square. Perimeter = 4 * 6 = 24. A 4x2 rectangle is cut from a corner. The two sides forming the internal corner replace the two original sides, adding 4+2 and removing 6. Wait, cutting from the inside surface increases the perimeter. The perimeter of the original square is 6+6+6+6=24. When a rectangle is cut from the corner, the two original sides at the corner are replaced by the two sides of the cut rectangle. Let's assume the corner was the top-right corner. Original perimeter segment is 6+6 (top and right). Cut rectangle is 4 wide and 2 high. The new perimeter segments are 6-4=2 (top remaining) + 2 (cut vertical) + 4 (cut horizontal) + 6-2=4 (right remaining). The other two sides (left and bottom) are still 6+6. So perimeter is 6 + (6-2) + 4 + 2 + (6-4) + 6 = 6 + 4 + 4 + 2 + 2 + 6 = 24. This is incorrect. Cutting a rectangle from a *corner* of a large rectangle/square results in replacing two segments with two equal-length segments, so the perimeter *does not change*. If the original square is 6x6, perimeter is 24. Cutting a 4x2 rectangle from a corner leaves an L shape. The sides are 6, 6, 6-2=4, 4, 2, 6-4=2. Perimeter = 6+6+4+4+2+2 = 24. So, Perimeter 1 = 24. Figure 2: U-shape. External bottom edge is 6. Two vertical arms are 4 high. The inner horizontal segment is 2 wide. The outer sides of the arms have width 2. The inner sides of the arms have width 2. The outer top edges of the arms are 2 wide. Perimeter = 6 (bottom) + 4 (left vertical outer) + 2 (left horizontal top) + 2 (left vertical inner) + 2 (inner horizontal gap) + 2 (right vertical inner) + 2 (right horizontal top) + 4 (right vertical outer) = 6 + 4 + 2 + 2 + 2 + 2 + 2 + 4 = 24. No, this does not match the structure. Let's recalculate based on the image. Bottom 6. Left vertical arm outer 4. Left horizontal top outer 2. Left vertical arm inner 4. Inner horizontal segment 2. Right vertical arm inner 4. Right horizontal top outer 2. Right vertical arm outer 4. Perimeter = 6 + 4 + 2 + 4 + 2 + 4 + 2 + 4 = 28. Figure 3: Step shape. Bottom 6. Right vertical 6. Top horizontal 2. Left vertical (top part) 2. Horizontal segment below that 4. Left vertical (bottom part) 4. Perimeter = 6 (bottom) + 6 (right vertical) + 2 (top horizontal) + 2 (left vertical top) + 4 (horizontal segment) + 4 (left vertical bottom) = 24. Let's re-examine the calculation for Figure 1 (L-shape). Perimeter of original square 6x6 is 24. Cut a 4x2 rectangle from a corner. The original corner had two sides meeting. These are replaced by the two sides of the cut rectangle. The original perimeter loses segments of length 4 and 2 but gains segments of length 4 and 2. So perimeter remains 24. Let's re-examine the calculation for Figure 2 (U-shape). Bottom 6. Two vertical segments of height 4. A horizontal segment connecting their tops is of length 2. The gap between the arms is 2. The width of each arm is (6-2)/2 = 2. Outer perimeter: 6 (bottom) + 4 (left vertical outer) + 2 (left top outer) + 2 (right top outer) + 4 (right vertical outer) = 6+4+2+2+4 = 18? No, this is wrong. Inner perimeter: 4 (left vertical inner) + 2 (inner horizontal gap) + 4 (right vertical inner) = 10. Total perimeter = outer + inner = 18+10 = 28. Let's re-examine Figure 3 (Step shape). Bottom 6. Left side vertical length is 4+2=6. Right side vertical length is 6. Top side horizontal length is 4+2=6. So it fits in a 6x6 square. Dimensions shown: Bottom 6. Right vertical 6. Top right horizontal 2. Top left vertical 2. Middle horizontal 4. Middle left vertical 4. Perimeter = 6 (bottom) + 6 (right) + 2 (top right horizontal) + 2 (top left vertical) + 4 (middle horizontal) + 4 (middle left vertical) = 24. Let's recheck Figure 1: Original 6x6 square. Cut 4x2. Perimeter = 6 + (6-2) + 4 + 2 + (6-4) + 6 = 6 + 4 + 4 + 2 + 2 + 6 = 24. This is incorrect. The perimeter of the L-shape: two sides of length 6, two sides of length 6-2=4, two sides of length 6-4=2. Perimeter = 6 + 6 + 4 + 2 + 2 + 4 = 24. Still 24. Let's rethink the perimeter change when cutting a rectangle from the edge/interior. Cutting a rectangular hole *inside* a shape increases the perimeter by the perimeter of the hole. Cutting a rectangular part from the *edge* (not corner) increases the perimeter by twice the sum of the sides of the rectangle cut. Cutting a rectangular part from the *corner* keeps the perimeter the same. Figure 1 is cutting from a corner. So Perimeter 1 = Original Perimeter = 6 * 4 = 24. Figure 2 is cutting from the middle of an edge (the top edge is cut). Original shape is 6x6. Cut is 4x2. Let's assume the top edge (length 6) is cut. The cut piece is 4x2. Imagine a 6x6 square. Cut a 4x2 rectangle from the middle of the top edge. The shape is now like a rectangle with a smaller rectangle removed from the top side, leaving a U-shape. The perimeter of the original square is 24. We remove a segment of length 4 from the top edge. We add the three sides of the removed rectangle: 4 (bottom of cut) + 2 (left side of cut) + 2 (right side of cut) = 8. The new perimeter = 24 - 4 + 8 = 28. So Perimeter 2 = 28. Figure 3 is cutting from the middle of two adjacent edges. Imagine a 6x6 square. Cut a 4x2 rectangle. This shape looks like a combination of rectangles. Bottom width 6. Right height 6. The step is at height 4 from the bottom, and extends 4 from the left. The remaining part to the right is 6-4=2 wide. The part above the step is 6-4=2 high. Perimeter = 6 (bottom) + 6 (right) + 2 (top right horizontal) + 2 (top left vertical) + 4 (middle horizontal) + 4 (middle left vertical) = 24. Let's verify the shape and dimensions again. Bottom is 6. Right side is 6. The top edge is broken into two segments, total length 4+2=6. The left edge is broken into two segments, total length 4+2=6. Perimeter = 6+6+6+6 = 24. Area calculation: Original Area = 6 * 6 = 36. Cut Area = 4 * 2 = 8. Remaining Area = 36 - 8 = 28. All three figures have the same area (28). Comparing perimeters: Perimeter 1 = 24, Perimeter 2 = 28, Perimeter 3 = 24. Comparing areas: Area 1 = 28, Area 2 = 28, Area 3 = 28. So, Perimeters are not all equal (24, 28, 24). Areas are all equal (28). The correct statement should compare these. **Options:** A. 周长相等, 面积相等 (Perimeter equal, Area equal) B. 周长相等, 面积不相等 (Perimeter equal, Area not equal) C. 周长不相等, 面积相等 (Perimeter not equal, Area equal) D. 周长不相等, 面积不相等 (Perimeter not equal, Area not equal) Based on the calculations: Perimeters are not equal (24, 28, 24). Areas are equal (28, 28, 28). So, Perimeters are unequal, and Areas are equal. This matches option C. **Question 2:** 2. (朝阳区)下图中的阴影部分的面积是 **(Translation):** 2. (Chaoyang District) The area of the shaded part in the figure below is **(Note):** The image for Question 2 is not fully visible. Only the question stem is present. **Other visible text/stamps:** There is a faint circular stamp-like watermark with text that appears to say "拒绝盗印" (Reject Piracy / Unauthorized Copying) and some other Chinese characters. There might be a school name or organization name. **Summary of extracted content:** * Title and introductory info. * Section header for Multiple Choice. * Question 1 stem. * Description of the three figures for Question 1 with labeled dimensions. * Calculated perimeters (24, 28, 24) and areas (28, 28, 28) for the figures based on the problem description and labels. * Options A, B, C, D for Question 1. * Question 2 stem (incomplete as the image is missing). * A watermark/stamp with text "拒绝盗印".