Practice calculating the area of irregular shapes by dividing them into rectangles.

Here are the step-by-step solutions for each problem on the worksheet. The strategy is to split each irregular shape into simple rectangles, find the area of each rectangle (Length × Width), and then add them together.

1. Top Left Shape
* Split: Divide the L-shape vertically into a tall rectangle on the left and a shorter rectangle on the right.
* Left Rectangle: The height is given as 5 cm. The width is 2 cm.
* Area = $5 \times 2 = 10 \text{ cm}^2$
* Right Rectangle: The total bottom width is 10 cm. Since the left part is 2 cm wide, the right part is $10 - 2 = 8 \text{ cm}$ wide. The height is given as 3 cm.
* Area = $8 \times 3 = 24 \text{ cm}^2$
* Total Area: $10 + 24 = 34 \text{ cm}^2$

2. Top Right Shape
* Split: Divide the shape horizontally into a top rectangle and a bottom rectangle.
* Top Rectangle: The length is 12 m. To find the height, look at the vertical sides: the total height on the right is 7 m, and the bottom section is 3 m high. So, the top height is $7 - 3 = 4 \text{ m}$.
* Area = $12 \times 4 = 48 \text{ m}^2$
* Bottom Rectangle: The total width is 12 m, and the cut-out section is 6 m. So, the width of this block is $12 - 6 = 6 \text{ m}$. The height is 3 m.
* Area = $6 \times 3 = 18 \text{ m}^2$
* Total Area: $48 + 18 = 66 \text{ m}^2$

3. Middle Left Shape
* Split: Divide vertically into a left rectangle and a right rectangle.
* Left Rectangle: Height is 5 cm, Width is 2 cm.
* Area = $5 \times 2 = 10 \text{ cm}^2$
* Right Rectangle: The total width is 10 cm. The left part is 2 cm, so the right width is $10 - 2 = 8 \text{ cm}$. The height is 4 cm.
* Area = $8 \times 4 = 32 \text{ cm}^2$
* Total Area: $10 + 32 = 42 \text{ cm}^2$

4. Middle Right Shape
* Split: Divide horizontally into a bottom rectangle and a top rectangle.
* Bottom Rectangle: Length is 11 cm, Height is 5 cm.
* Area = $11 \times 5 = 55 \text{ cm}^2$
* Top Rectangle: The total height on the left is 9 cm. The bottom part is 5 cm, so the top height is $9 - 5 = 4 \text{ cm}$. The total width is 11 cm, and the left "stem" is 6 cm, so the top width is $11 - 6 = 5 \text{ cm}$.
* Area = $5 \times 4 = 20 \text{ cm}^2$
* Total Area: $55 + 20 = 75 \text{ cm}^2$

5. Bottom Left Shape
* Split: Divide vertically into three rectangles: Left, Middle, and Right.
* Left Rectangle: Height 5 cm, Width 2 cm. Area = $10 \text{ cm}^2$.
* Right Rectangle: Same dimensions as the left. Area = $10 \text{ cm}^2$.
* Middle Rectangle: The total width is 8 cm. Subtracting the left (2) and right (2) widths leaves $8 - 4 = 4 \text{ cm}$ for the middle width. The height is 3 cm. Area = $4 \times 3 = 12 \text{ cm}^2$.
* Total Area: $10 + 10 + 12 = 32 \text{ cm}^2$

6. Bottom Right Shape
* Split: Divide vertically into a Left Block, a Right Block, and a small connecting Middle Block.
* Left Block: Height 5 cm, Width 2 cm. Area = $10 \text{ cm}^2$.
* Right Block: Height 4 cm, Width 3 cm. Area = $12 \text{ cm}^2$.
* Middle Block: The total width is 11 cm. Subtracting the left (2) and right (3) widths leaves $11 - 5 = 6 \text{ cm}$ for the middle width. The height is 2 cm. Area = $6 \times 2 = 12 \text{ cm}^2$.
* Total Area: $10 + 12 + 12 = 34 \text{ cm}^2$

Challenge Problem
* Method: This is a large rectangle with a smaller rectangular hole inside. Calculate the area of the big rectangle and subtract the area of the hole.
* Large Rectangle: Length 11 cm, Width 6 cm.
* Area = $11 \times 6 = 66 \text{ cm}^2$
* Hole: Length 6 cm, Width 2 cm.
* Area = $6 \times 2 = 12 \text{ cm}^2$
* Total Area: $66 - 12 = 54 \text{ cm}^2$

Final Answer:
1. 34 cm²
2. 66 m²
3. 42 cm²
4. 75 cm²
5. 32 cm²
6. 34 cm²
Challenge: 54 cm²