1. **Problem statement:** We have two square sheets of paper, each 6 cm by 6 cm. From each square, a rectangular notch is cut out. For figure A, the notch measures 2 cm by 3 cm from the lower-left corner. For figure B, the notch measures 2 cm by 3 cm from the upper-left corner. We need to find the area and perimeter of the remaining shape for each figure and observe what we notice. 2. **Formulas and rules:** - Area of a rectangle: $\text{Area} = \text{length} \times \text{width}$ - Perimeter of a polygon: sum of the lengths of all sides. - When a rectangular notch is cut out, the remaining area is the original area minus the notch area. - The perimeter changes because the notch adds extra edges. 3. **Calculations for figure A:** - Original square area: $$6 \times 6 = 36$$ cm$^2$ - Notch area: $$2 \times 3 = 6$$ cm$^2$ - Remaining area: $$36 - 6 = 30$$ cm$^2$ - Original perimeter: $$4 \times 6 = 24$$ cm - The notch adds two new edges inside the square: 2 cm and 3 cm. - The original side of 6 cm on the left is now split into three parts: 2 cm notch depth, 3 cm notch height, and remaining 1 cm. - The new perimeter is: $$6 + 6 + 6 + 6 - 2 - 3 + 2 + 3 = 24 - 5 + 5 = 24$$ cm (Because the notch removes 2 cm and 3 cm from the original edges but adds the same lengths as new edges.) 4. **Calculations for figure B:** - Original square area: $$6 \times 6 = 36$$ cm$^2$ - Notch area: $$2 \times 3 = 6$$ cm$^2$ - Remaining area: $$36 - 6 = 30$$ cm$^2$ - Original perimeter: $$24$$ cm - The notch again adds two new edges of lengths 2 cm and 3 cm. - The perimeter calculation is the same as figure A: $$24$$ cm 5. **Observation:** - Both figures have the same remaining area: $$30$$ cm$^2$ - Both figures have the same perimeter: $$24$$ cm - Cutting out the rectangular notch reduces the area by the notch area but does not change the perimeter because the notch edges replace parts of the original edges. **Final answers:** - Figure A: Area = $30$ cm$^2$, Perimeter = $24$ cm - Figure B: Area = $30$ cm$^2$, Perimeter = $24$ cm