Irregular Shape Area & Perimeter

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📐 Part 1: Find the Area

Decompose each irregular shape into rectangles. Show your working and include the correct square units.

1. Shape A: A 10 m by 7 m rectangle has a 4 m by 3 m rectangle removed from its top-right corner. Find the area.

2. Shape B: A T-shape is made from a 9 m by 2 m rectangle and a 3 m by 6 m rectangle joined below its centre. Find the total area.

3. Shape C: A 12 cm by 8 cm rectangle has a 4 cm by 3 cm rectangular notch cut from the middle of one side. Find the remaining area.

4. Shape D: A stair-shaped figure is made from three rectangles: 10 cm by 2 cm, 7 cm by 3 cm, and 4 cm by 3 cm. Find the total area.

5. Shape E: An L-shaped garden is formed from a 14 m by 9 m rectangle with a 5 m by 4 m corner removed. Find the area of the garden.

📏 Part 2: Find the Area and Perimeter

For each shape, calculate both the area and the perimeter. Remember that perimeter is the distance around the outside.

6. Shape F: An L-shape has an outside length of 11 m and an outside height of 8 m. A 4 m by 3 m rectangle is removed from the bottom-left corner. Find its area and perimeter.

7. Shape G: A 10 cm by 6 cm rectangle has a 2 cm by 2 cm square added to the centre of its top side. Find the total area and perimeter.

8. Shape H: A 15 m by 10 m rectangle has a 5 m by 4 m rectangular section removed from one corner. Find the area and perimeter of the remaining shape.

9. Shape I: A step-shaped figure has side lengths around its boundary of 12 cm, 3 cm, 4 cm, 3 cm, 4 cm, 3 cm, 4 cm and 6 cm. Its area is made from rectangles measuring 12 cm by 3 cm, 8 cm by 3 cm and 4 cm by 3 cm. Find the area and perimeter.

10. Design challenge: Draw an irregular shape made from at least three rectangles. Label every side length. Calculate its area and perimeter.