Worksheet for calculating the area of rectilinear figures using grid squares.

To find the area of each shaded rectilinear figure, we count the number of unit squares that are shaded. Each small square represents 1 square unit ($1 \text{ m}^2$).

Here is the step-by-step count for each problem:

1.
- Top row: 3 squares
- Middle row: 3 squares (center one overlaps with top/bottom visually, but let's count distinct blocks)
- Let's count individually:
- Vertical column in the middle: 4 squares high.
- Horizontal arms on the second square from top: 1 left, 1 right.
- Total = $4 + 1 + 1 = 6$.
- Area = 6 m²

2.
- It is a vertical rectangle.
- Height: 5 squares.
- Width: 2 squares.
- Total = $5 \times 2 = 10$.
- Area = 10 m²

3.
- Top row: 4 squares.
- Second row: 2 squares (on the right).
- Third row: 2 squares (on the right).
- Fourth row: 2 squares (on the right).
- Let's recount carefully.
- Row 1: 4 shaded.
- Row 2: 2 shaded (right side).
- Row 3: 2 shaded (right side).
- Row 4: 2 shaded (right side).
- Total = $4 + 2 + 2 + 2 = 10$.
- Area = 10 m²

4.
- Left vertical part: 3 squares high, 1 wide.
- Bottom horizontal part extending right: 2 squares.
- Let's trace it:
- Column 1: Rows 2,3,4 are shaded (3 squares). Note: Row 1 is empty. Wait, looking closely at #4.
- It looks like an 'L' shape rotated.
- Vertical bar on left: 3 squares tall.
- Horizontal bar at bottom: extends 2 more squares to the right.
- Total = $3 (\text{vertical}) + 2 (\text{horizontal extension}) = 5$.
- Area = 5 m²

5.
- This is a large square with a corner missing? No, it's a shape inside a grid.
- Let's count the shaded squares directly.
- Left column: 4 squares.
- Next column: 3 squares (bottom 3).
- Next column: 2 squares (bottom 2).
- Right column: 1 square (bottom 1).
- Total = $4 + 3 + 2 + 1 = 10$.
- Area = 10 m²

6.
- A rectangular block.
- Height: 4 squares.
- Width: 3 squares.
- Total = $4 \times 3 = 12$.
- Area = 12 m²

7.
- Left block: 3 wide, 3 high = 9 squares.
- Right extension: attached to the bottom right? No, let's look closer.
- It looks like a 3x3 square on the left.
- And a 1x3 vertical strip on the right? Or a 3x1 horizontal?
- Let's re-examine image #7.
- It appears to be a 3x3 square (9 units) plus a 1x3 vertical column attached to the right side? No, the grid lines show:
- Columns 1-3 are filled for rows 1-3. That's 9.
- Column 4 has squares in rows 1, 2, 3? No, looking at the shading, it seems to be a 3x3 square and then a 1-unit wide by 3-unit high strip next to it?
- Actually, let's look at the shape again. It looks like a "U" or a bracket?
- Let's count individual squares.
- Row 1: 4 squares.
- Row 2: 2 squares (first and last).
- Row 3: 2 squares (first and last).
- Row 4: 4 squares.
- This interpretation assumes a hollow center. Let's look really closely at crop 4 and 7.
- Crop 4 shows #7 clearly.
- It is a 4x4 grid area.
- Shaded:
- Row 1: All 4 shaded.
- Row 2: First and Last shaded (2).
- Row 3: First and Last shaded (2).
- Row 4: All 4 shaded.
- Total = $4 + 2 + 2 + 4 = 12$.
- Area = 12 m²

8.
- An L-shape.
- Vertical part: 4 squares high, 1 wide.
- Horizontal part: Extends 3 squares to the right from the bottom.
- The corner square is shared.
- Vertical (excluding corner): 3 squares.
- Horizontal (including corner): 4 squares.
- Total = $3 + 4 = 7$.
- Alternatively: Column 1 has 4. Columns 2,3,4 have 1 each at the bottom. $4 + 1 + 1 + 1 = 7$.
- Area = 7 m²

9.
- Two separate rectangles? Or one connected shape?
- It looks like two vertical bars connected by a bridge?
- Let's count.
- Left bar: 1 wide, 4 high = 4 squares.
- Right bar: 1 wide, 4 high = 4 squares.
- Connecting bridge in the middle row?
- Looking at #9 in the original image:
- It looks like a "H" shape or two parallel lines.
- Left column: 4 shaded.
- Right column: 4 shaded.
- Are they connected? There is no shading between them.
- So it is two separate strips.
- Total = $4 + 4 = 8$.
- Area = 8 m²

10.
- A stepped shape.
- Bottom row: 4 squares.
- Second row up: 3 squares.
- Third row up: 2 squares.
- Top row: 1 square.
- Total = $4 + 3 + 2 + 1 = 10$.
- Area = 10 m²

11.
- A cross shape?
- Center column: 5 squares high.
- Left arm: 1 square.
- Right arm: 1 square.
- The arms are attached to the center square (3rd one down).
- Total = $5 (\text{center}) + 1 (\text{left}) + 1 (\text{right}) = 7$.
- Area = 7 m²

12.
- A green shape.
- It looks like a zig-zag or stairs.
- Let's count the squares.
- Top-left pair: 2 squares.
- Step down-right: 2 squares.
- Step down-right: 2 squares.
- Step down-right: 2 squares.
- Let's trace carefully.
- Row 1: Squares 1,2 shaded.
- Row 2: Square 2 is already counted? No, Row 1 is top.
- Let's assume standard grid orientation.
- Block 1 (top left): 2x1 horizontal? No, looks like 2x2 block shifted?
- Let's count individual shaded units.
- There are 4 distinct 2-square blocks arranged diagonally.
- Block 1: Top-left corner. 2 squares.
- Block 2: Connected to bottom-right of Block 1?
- Let's just count every shaded square.
- 1, 2 (top row)
- 3, 4 (second row, shifted right by 1)
- 5, 6 (third row, shifted right by 1)
- 7, 8 (fourth row, shifted right by 1)
- Total = 8 squares.
- Area = 8 m²

Final Answer:
1. 6 m²
2. 10 m²
3. 10 m²
4. 5 m²
5. 10 m²
6. 12 m²
7. 12 m²
8. 7 m²
9. 8 m²
10. 10 m²
11. 7 m²
12. 8 m²