1. **Problem a:** Find the side length of a square with perimeter 20 cm. 2. The formula for the perimeter of a square is $$P = 4s$$ where $s$ is the side length. 3. Given $P = 20$, solve for $s$: $$20 = 4s$$ Divide both sides by 4: $$s = \frac{20}{4} = 5$$ Each side of the square is 5 cm. 4. **Problem b:** Find the perimeter of the shape formed by cutting an equilateral triangle from a rectangle. 5. The rectangle has height 8.1 cm and width 11 cm. 6. The equilateral triangle is cut from the right side, so one side of the triangle equals the height of the rectangle, 8.1 cm (since the triangle is equilateral, all sides are equal). 7. The original rectangle perimeter is: $$P_{rect} = 2(8.1 + 11) = 2(19.1) = 38.2$$ 8. After cutting the triangle, the right side of the rectangle is replaced by two sides of the triangle forming an inward notch. 9. The new perimeter is the sum of: - Left side: 8.1 cm - Top side: 11 cm - Bottom side: 11 cm - Two sides of the triangle (each 8.1 cm) 10. Calculate the new perimeter: $$P = 8.1 + 11 + 11 + 8.1 + 8.1 = 46.3$$ **Final answers:** - a) Each side of the square is 5 cm. - b) The perimeter of the new shape is 46.3 cm.