1. **Problem statement:** Find the perimeter and area of the given shapes (a) through (f). 2. **Formulas and rules:** - Perimeter is the sum of all side lengths. - Area depends on the shape; for composite shapes, divide into rectangles or squares, find each area, then sum. --- ### (a) L-shape (top-left) - Sides: 3cm (top), 3cm (inner vertical), 3cm (middle horizontal), 4cm (right vertical), 6cm (bottom), 7cm (left vertical) - **Perimeter:** Sum all sides: $$3 + 3 + 3 + 4 + 6 + 7 = 26\text{ cm}$$ - **Area:** Split into two rectangles: - Rectangle 1: width 3cm, height 7cm - Rectangle 2: width 3cm, height 4cm Area = $$3 \times 7 + 3 \times 4 = 21 + 12 = 33\text{ cm}^2$$ --- ### (b) U-like notch shape (top-right) - Sides: 8m (left), 2m (top notch width), 4m (inner vertical), 3m + 3m (bottom segments) - **Perimeter:** Sum all sides: $$8 + 2 + 4 + 3 + 3 + 8 = 28\text{ m}$$ (Note: The right side equals left side 8m to close shape) - **Area:** Split into rectangle minus notch: - Large rectangle: width 8m, height 8m - Notch rectangle: width 2m, height 4m Area = $$8 \times 8 - 2 \times 4 = 64 - 8 = 56\text{ m}^2$$ --- ### (c) Stepped shape (top-right) - Sides: 5m (left vertical), 2m (notch step), 2m (inner drop), 6m (bottom) - **Perimeter:** Sum all sides: $$5 + 2 + 2 + 6 + 5 + 6 = 26\text{ m}$$ (assuming shape closes with 5m right vertical and 6m top horizontal) - **Area:** Split into two rectangles: - Rectangle 1: 5m by 6m - Rectangle 2: 2m by 2m Area = $$5 \times 6 + 2 \times 2 = 30 + 4 = 34\text{ m}^2$$ --- ### (d) Rectangle with bump (bottom-left) - Sides: 18cm (base), 15cm (left side), 4cm segments on top bump - **Perimeter:** Sum all sides: $$18 + 15 + 4 + 4 + 4 + 15 + 18 = 78\text{ cm}$$ - **Area:** Large rectangle plus bump: - Large rectangle: 18cm by 15cm - Bump: 4cm by 4cm Area = $$18 \times 15 + 4 \times 4 = 270 + 16 = 286\text{ cm}^2$$ --- ### (e) Notched rectangle (center) - Sides: 9cm (top), 6cm (left), 1cm and 3cm inner steps, 6cm (right) - **Perimeter:** Sum all sides: $$9 + 6 + 1 + 3 + 6 + 9 = 34\text{ cm}$$ (assuming bottom side equals top 9cm) - **Area:** Split into rectangles: - Main rectangle: 9cm by 6cm - Notch rectangles: 1cm by 3cm Area = $$9 \times 6 - 1 \times 3 = 54 - 3 = 51\text{ cm}^2$$ --- ### (f) T-shape (bottom-right) - Sides: 10m (base), 3m (right side), 4m (top-left horizontal), 2m (top bar width), 6m (stem height) - **Perimeter:** Sum all sides: $$10 + 3 + 4 + 2 + 6 + 10 + 3 = 38\text{ m}$$ (assuming shape closes with matching sides) - **Area:** Split into rectangles: - Top bar: 10m by 2m - Stem: 6m by 4m Area = $$10 \times 2 + 6 \times 4 = 20 + 24 = 44\text{ m}^2$$ --- **Final answers:** - (a) Perimeter = 26 cm, Area = 33 cm² - (b) Perimeter = 28 m, Area = 56 m² - (c) Perimeter = 26 m, Area = 34 m² - (d) Perimeter = 78 cm, Area = 286 cm² - (e) Perimeter = 34 cm, Area = 51 cm² - (f) Perimeter = 38 m, Area = 44 m²