Overlapping Squares A5A673

1. **Problem 1: Calculate the perimeter of the whole diagram with two overlapping squares of sides 8 cm and 2 cm.** 2. The perimeter of a square is given by the formula $$P = 4 \times \text{side}$$. 3. For the larger square with side 8 cm, the perimeter is $$4 \times 8 = 32\text{ cm}$$. 4. For the smaller square with side 2 cm, the perimeter is $$4 \times 2 = 8\text{ cm}$$. 5. Since the squares overlap, the overlapping side length is 2 cm (the smaller square's side). 6. The total perimeter of the combined figure is the sum of the perimeters minus twice the overlapping side (because the overlapping side is counted twice in the sum): $$P_{total} = 32 + 8 - 2 \times 2 = 40 - 4 = 36\text{ cm}$$. --- 7. **Problem 2: Prove that shapes A and B have equal perimeter given sides 5 cm, 6 cm, x cm, y cm for A and 2 cm, 3 cm, x cm, y cm for B.** 8. The perimeter of shape A is $$P_A = 5 + 6 + x + y$$. 9. The perimeter of shape B is $$P_B = 2 + 3 + x + y$$. 10. Simplify both: $$P_A = 11 + x + y$$ $$P_B = 5 + x + y$$ 11. To prove $$P_A = P_B$$, we need to show $$11 + x + y = 5 + x + y$$. 12. Subtract $$x + y$$ from both sides: $$11 = 5$$ 13. This is false, so the perimeters are not equal unless the problem implies something else or the values of $$x$$ and $$y$$ adjust accordingly. --- 14. **Problem 3: The diagram shows two shapes, A and B. Prove that both of the shapes have equal perimeter with given lengths 80 m, 100 m, 180 m, P.** 15. Without additional information or a diagram, we cannot prove equality of perimeters. **Final answer for Problem 1:** The perimeter of the whole diagram is $$36\text{ cm}$$.