1. **State the problem:** We have a rectangle where the length is 7 cm longer than the width. Four such rectangles are arranged to form an 8-sided shape with a total perimeter of 70 cm. We need to find the area of this 8-sided shape. 2. **Define variables:** Let the width of the rectangle be $w$ cm. Then the length is $w + 7$ cm. 3. **Understand the shape and perimeter:** The 8-sided shape is formed by 4 rectangles arranged so that some sides overlap. The perimeter of the shape is given as 70 cm. 4. **Express the perimeter of the 8-sided shape:** The shape consists of 4 rectangles arranged in a pattern where the total perimeter is not simply $4 \times$ perimeter of one rectangle. 5. **Calculate the perimeter of one rectangle:** Perimeter of one rectangle = $2(w + (w+7)) = 2(2w + 7) = 4w + 14$. 6. **Analyze the 8-sided shape perimeter:** The 8-sided shape is formed by placing two rectangles vertically on the left and right, and two horizontally on top and middle. The total perimeter is the sum of the outer edges. 7. **Calculate the total perimeter in terms of $w$:** The vertical sides of the shape are the sum of the lengths of the two vertical rectangles: $2(w+7)$. The horizontal sides are the sum of the widths of the two horizontal rectangles: $2w$. So, perimeter $P = 2 \times$ (vertical height) $+ 2 \times$ (horizontal width) = $2 \times 2(w+7) + 2 \times 2w = 4(w+7) + 4w = 4w + 28 + 4w = 8w + 28$. 8. **Set perimeter equal to 70 and solve for $w$:** $$8w + 28 = 70$$ $$8w = 70 - 28$$ $$8w = 42$$ $$w = \frac{42}{8} = \frac{21}{4} = 5.25$$ 9. **Find the length:** $$\text{length} = w + 7 = 5.25 + 7 = 12.25$$ 10. **Calculate the area of one rectangle:** $$\text{Area} = w \times (w + 7) = 5.25 \times 12.25 = 64.3125$$ 11. **Calculate the area of the 8-sided shape:** Since the 8-sided shape is made of 4 rectangles without overlapping area, $$\text{Total area} = 4 \times 64.3125 = 257.25$$ **Final answer:** The area of the 8-sided shape is $257.25$ square centimeters.