Area Of Irregular Shapes Worksheet - Free Printable

Here are the step-by-step solutions for each shape. To find the area of these L-shaped or complex rectilinear shapes, we split them into two simple rectangles, calculate the area of each, and then add them together.

1) Shape 1
* Split the shape: We can divide this into a bottom rectangle and a top rectangle.
* Bottom Rectangle: The total width at the bottom is not explicitly given as a single number, but looking at the top widths ($1\text{ cm} + 3\text{ cm}$), the total width is $4\text{ cm}$. The height of the left side is $2\text{ cm}$. So, the bottom rectangle is $4\text{ cm}$ wide and $2\text{ cm}$ high.
* Area = $4 \times 2 = 8\text{ cm}^2$.
* Top Rectangle: This sits on top of the right side. Its width is $3\text{ cm}$. Its height is the total right height ($3\text{ cm}$) minus the bottom height ($2\text{ cm}$), which is $1\text{ cm}$.
* Area = $3 \times 1 = 3\text{ cm}^2$.
* Total Area: $8 + 3 = 11\text{ cm}^2$.

*(Alternative Split: Left vertical rectangle $1 \times 3 = 3$, Right vertical rectangle $3 \times 2 = 6$. Total $3+6=9$? Wait, let's re-read the diagram carefully.)*

Let's look closer at Shape 1 labels:
- Left vertical edge: $2\text{ cm}$
- Top-left horizontal edge: $1\text{ cm}$
- Top-right horizontal edge (indent): $3\text{ cm}$
- Right vertical edge: $3\text{ cm}$

Let's split it vertically into two rectangles:
1. Left Rectangle: Width is $1\text{ cm}$. Height is the full left side, which is $2\text{ cm}$? No, the label $2\text{ cm}$ is on the left vertical edge. The label $3\text{ cm}$ is on the right vertical edge.
Let's assume the shape is composed of a left block and a right block.
- Left block width: $1\text{ cm}$. Height: The left edge is labeled $2\text{ cm}$. But wait, usually these diagrams imply parallel lines. If the right edge is $3\text{ cm}$ and the left is $2\text{ cm}$, there is a step.
- Let's try splitting horizontally.
- Bottom Rectangle: Spans the full width. The total width is the sum of the top segments: $1\text{ cm} + 3\text{ cm} = 4\text{ cm}$. The height of the left side is $2\text{ cm}$. Is the bottom part $2\text{ cm}$ high all the way across? The right side is $3\text{ cm}$ tall. So the "bottom" rectangle would be $4\text{ cm}$ wide by $2\text{ cm}$ high. Area = $8\text{ cm}^2$.
- Top Rectangle: Sits on the right side. Width is $3\text{ cm}$. Height is total right height ($3\text{ cm}$) minus bottom height ($2\text{ cm}$) = $1\text{ cm}$. Area = $3 \times 1 = 3\text{ cm}^2$.
- Total Area = $8 + 3 = 11\text{ cm}^2$.

Let's double check with a vertical split.
- Left Rectangle: Width $1\text{ cm}$. Height $2\text{ cm}$. Area = $2\text{ cm}^2$.
- Right Rectangle: Width $3\text{ cm}$. Height $3\text{ cm}$. Area = $9\text{ cm}^2$.
- Total Area = $2 + 9 = 11\text{ cm}^2$.
Both methods give 11.

2) Shape 2
* Labels: Left edge $6\text{ cm}$, Bottom edge $4\text{ cm}$, Right lower edge $2\text{ cm}$, Right upper edge $4\text{ cm}$ (vertical).
* Let's deduce missing lengths.
- Total height on the left is $6\text{ cm}$.
- The right side has a vertical segment of $4\text{ cm}$ at the top? Or is the $4\text{ cm}$ label for the top horizontal part? Looking at the orientation, the $4\text{ cm}$ is next to the top-right vertical drop. The $2\text{ cm}$ is the bottom-right vertical rise? No, standard notation:
- Left vertical: $6\text{ cm}$
- Bottom horizontal: $4\text{ cm}$
- Right-most vertical (lower part): $2\text{ cm}$
- Inner vertical (upper part): $4\text{ cm}$? That doesn't add up ($2+4=6$). Yes, it does.
- So we have a large rectangle on the left and a smaller one on the right? Or top and bottom?
- Let's split it into two vertical rectangles.
- We need the width of the top part. It's not given directly.
- Let's split it into two horizontal rectangles instead.
- Bottom Rectangle: Width is $4\text{ cm}$. Height is the right-most vertical edge, which is $2\text{ cm}$. Area = $4 \times 2 = 8\text{ cm}^2$.
- Top Rectangle: Sits on top of the left part. The total height is $6\text{ cm}$. The bottom part is $2\text{ cm}$ high. So the top part is $6 - 2 = 4\text{ cm}$ high. What is its width? The label "$4\text{ cm}$" is on the right vertical edge of the top section. This implies the top section has a height of $4\text{ cm}$. We still need the width.
- Wait, let's look at the labels again.
- Left side: $6\text{ cm}$ (Total Height)
- Bottom side: $4\text{ cm}$ (Total Width)
- Right side lower vertical: $2\text{ cm}$
- Right side upper vertical (the inner corner drop?): $4\text{ cm}$.
- This implies the top block has a height of $4\text{ cm}$ and the bottom block has a height of $2\text{ cm}$. $4+2=6$, which matches the left side.
- We need the width of the top block. It is not explicitly given. However, usually in these problems, if a dimension is missing, it might be inferred or I am misinterpreting the label positions.
- Let's re-examine image 2.
- Left vertical: $6\text{ cm}$.
- Bottom horizontal: $4\text{ cm}$.
- Right vertical (bottom part): $2\text{ cm}$.
- Top horizontal: Not labeled.
- Inner vertical: $4\text{ cm}$.
- Inner horizontal: Not labeled.
- Actually, looking at the layout, the "$4\text{ cm}$" label is on the top horizontal edge? No, it's vertical text. It's likely the height of that upper segment.
- Is it possible the shape is split into a left rectangle and a right rectangle?
- If we split vertically:
- Left Rectangle: Height $6\text{ cm}$. Width? Unknown.
- Right Rectangle: Height $2\text{ cm}$. Width? Unknown.
- Let's look at the example provided in the worksheet header. It gives all necessary dimensions.
- Let's assume the label "$4\text{ cm}$" on the right refers to the width of the top protrusion? No, it's aligned vertically.
- Let's assume the label "$4\text{ cm}$" on the right refers to the height of the top section. Then the bottom section height is $2\text{ cm}$. Total height $6\text{ cm}$. This fits.
- We still need a width. The bottom width is $4\text{ cm}$. Is the top width the same? No, it's an L-shape.
- Is it possible the "$4\text{ cm}$" label at the bottom is the width of the left part? And the right part width is missing?
- Let's look really closely at crop 2.
- Left edge: $6\text{ cm}$.
- Bottom edge: $4\text{ cm}$.
- Right edge (lower): $2\text{ cm}$.
- Inner vertical edge: $4\text{ cm}$.
- There is no horizontal label for the top or the inner step.
- Wait, look at the position of the "$4\text{ cm}$" label on the right. It is next to the upper vertical segment.
- Look at the "$2\text{ cm}$" label. It is next to the lower vertical segment.
- Look at the "$4\text{ cm}$" label at the bottom. It spans the entire bottom width.
- Is there a label I'm missing? Maybe the top horizontal width is equal to something?
- Let's reconsider the shape. Maybe it's a large rectangle with a piece missing?
- Total bounding box: Width $4\text{ cm}$, Height $6\text{ cm}$. Area = $24\text{ cm}^2$.
- Missing piece is top-right.
- Height of missing piece: The left is $6$, the right lower is $2$. So the "cutout" starts at height $2$. The top of the cutout is at height $6$. So cutout height is $4\text{ cm}$.
- Width of missing piece: We need the width of the solid part on the left.
- This interpretation also requires a missing dimension.

- Alternative Interpretation:
- Maybe the "$4\text{ cm}$" at the bottom is NOT the total width. Maybe it's the width of the left column?
- If the bottom label "$4\text{ cm}$" applies only to the left vertical column's width...
- And the right part sticks out?
- Let's look at the alignment. The line for "$4\text{ cm}$" seems to span the whole bottom.

- Let's look at similar problems online. Often, if a dimension is missing, it might be symmetric or implied. But here, let's look at label 4) in the original image. It has $6\text{ cm}$, $5\text{ cm}$, $10\text{ cm}$, $2\text{ cm}$.
- Let's go back to 2). Is it possible the top horizontal width is meant to be inferred?
- What if the "$4\text{ cm}$" label on the right is actually the width of the top block? It is written vertically, but sometimes formatting is weird. If the top block width is $4\text{ cm}$, and the total width is $4\text{ cm}$ (from bottom label), then the left block width would be $0$, which is impossible.

- Let's try another read:
- Left Height: $6\text{ cm}$.
- Bottom Width: $4\text{ cm}$.
- Right Lower Height: $2\text{ cm}$.
- Inner Horizontal Width: Is the "$4\text{ cm}$" label actually pointing to the inner horizontal shelf? No, it's clearly vertical.

- Let's look at the spacing. The "$4\text{ cm}$" label is between the top edge and the inner corner. The "$2\text{ cm}$" label is between the inner corner and the bottom edge.
- This confirms heights: Top part height = $4\text{ cm}$, Bottom part height = $2\text{ cm}$.
- We are missing the width of the top part or the left part.
- However, look at the visual proportions. The left vertical bar looks wider than the right stub? Or vice versa?
- Let's look at Problem 1 again. Widths were $1$ and $3$. Heights $2$ and $3$.
- Let's look at Problem 3. Labels: Left $3\text{ cm}$, Top-left indent $2\text{ cm}$, Right $4\text{ cm}$, Bottom $6\text{ cm}$.
- Here, Bottom ($6$) is total width. Left ($3$) is partial height? Or total left height? Usually outer edges are total. So Left Height = $3$? But Right Height = $4$? That would mean the bottom isn't flat or top isn't flat.
- Actually, in Problem 3: Left edge is $3\text{ cm}$. Right edge is $4\text{ cm}$. Bottom is $6\text{ cm}$. Top-left horizontal is $2\text{ cm}$.
- This implies the shape is taller on the right.
- Split vertically:
- Left Rect: Width $2\text{ cm}$. Height $3\text{ cm}$. Area = $6$.
- Right Rect: Width = Total ($6$) - Left ($2$) = $4\text{ cm}$. Height = $4\text{ cm}$. Area = $16$.
- Total = $22$.
- Split horizontally:
- Bottom Rect: Width $6\text{ cm}$. Height $3\text{ cm}$ (matching left side). Area = $18$.
- Top Rect: Sits on right. Width $4\text{ cm}$. Height = Total Right ($4$) - Bottom ($3$) = $1\text{ cm}$. Area = $4$.
- Total = $18 + 4 = 22$.
- This logic holds up perfectly for #3.

- Now back to #2 with this confidence.
- Outer Left Height: $6\text{ cm}$.
- Outer Bottom Width: $4\text{ cm}$.
- Outer Right Lower Height: $2\text{ cm}$.
- Inner Vertical Height: $4\text{ cm}$. (This confirms the upper part is $4\text{ cm}$ tall, since $2+4=6$).
- We are missing a width dimension.
- Is it possible the "$4\text{ cm}$" label at the bottom is just the width of the left vertical section?
- If Left Width = $4\text{ cm}$, we still need the right width.
- Is it possible the "$4\text{ cm}$" label on the right is the width of the top section?
- If Top Width = $4\text{ cm}$, and Total Width = $4\text{ cm}$ (from bottom), then Left Width = $0$. Impossible.
- Let's look at the label placement in #2 again very carefully.
- The "$4\text{ cm}$" at the bottom is centered under the left part? No, it looks centered under the whole shape.
- The "$4\text{ cm}$" on the right is next to the top vertical segment.
- Is there a label on the top horizontal edge? No.
- Is there a label on the inner horizontal edge? No.

- Hypothesis: In some worksheets, if a dimension looks like a square, it might be assumed? No.
- Let's look at the numbers. $6, 4, 2, 4$.
- Could the top horizontal width be $2\text{ cm}$? (Just a guess based on visual symmetry with the $2\text{ cm}$ height?)
- Could the left vertical width be $2\text{ cm}$?

- Let's re-read the prompt image source or style. "WorksheetZone".
- Let's look at Problem 4.
- Top: $6\text{ cm}$. Left: $5\text{ cm}$. Bottom: $10\text{ cm}$. Right: $2\text{ cm}$.
- Split Vertically:
- Left Rect: Width $6\text{ cm}$. Height $5\text{ cm}$. Area = $30$.
- Right Rect: Width = $10 - 6 = 4\text{ cm}$. Height = $2\text{ cm}$. Area = $8$.
- Total = $38$.
- Split Horizontally:
- Bottom Rect: Width $10\text{ cm}$. Height $2\text{ cm}$. Area = $20$.
- Top Rect: Width $6\text{ cm}$. Height = $5 - 2 = 3\text{ cm}$. Area = $18$.
- Total = $20 + 18 = 38$.
- This works perfectly. All dims needed were present or derivable.

- So, Problem 2 MUST have all dimensions present. Which one am I misinterpreting?
- Labels:
- Left: $6\text{ cm}$
- Bottom: $4\text{ cm}$
- Right (lower): $2\text{ cm}$
- Right (upper/inner): $4\text{ cm}$
- There is NO horizontal dimension for the top part or the split.
- WAIT. Look at the "$4\text{ cm}$" label on the right side of shape 2.
- Look at the "$2\text{ cm}$" label below it.
- Look at the "$4\text{ cm}$" label at the bottom.
- Is it possible the shape is symmetric or the top width equals the bottom width of the other part?
- Let's look at the text color or font.
- Maybe the "$4\text{ cm}$" at the bottom is the width of the protruding part? No, it's under the main body.

- Let's consider that I might be misidentifying which edge the labels apply to.
- What if the "$4\text{ cm}$" label on the right is actually the width of the top horizontal edge?
- It is written vertically. But in problem 1, the "$3\text{ cm}$" width was written horizontally. In problem 3, "$2\text{ cm}$" width was horizontal. In problem 4, "$6\text{ cm}$" width was horizontal.
- Therefore, vertical text almost certainly indicates height.

- Is it possible the bottom "$4\text{ cm}$" is the width of the left rectangle only?
- If Left Width = $4\text{ cm}$, and we assume the right part has a width... still unknown.

- Let's look at the visual aspect ratio.
- In Shape 2, the left vertical bar looks roughly square-ish? If Height is $6$, Width shouldn't be $4$ if it's the whole thing?
- If the total width is $4$, and total height is $6$.
- The cut-out is on the top right.
- Height of cut-out = $4$. Height of remaining bottom = $2$.
- Width of cut-out = ?

- Is there a typo in my reading?
- Let's look at the label between the two vertical segments on the right.
- There is a label "$4\text{ cm}$" and a label "$2\text{ cm}$".
- There is a label "$6\text{ cm}$" on the left.
- There is a label "$4\text{ cm}$" on the bottom.

- Let's try one more possibility: The top horizontal width is equal to the bottom horizontal width of the "empty" space? No.

- Let's assume the question implies that the top horizontal width is the same as the right lower vertical height? ($2\text{ cm}$)? No logic for that.
- Let's assume the left vertical width is the same as the right lower vertical height? ($2\text{ cm}$)?
- If Left Width = $2\text{ cm}$:
- Left Rect: $2 \times 6 = 12$.
- Right Rect: Width = $4 - 2 = 2$. Height = $2$. Area = $4$.
- Total = $16$.
- Check with horizontal split:
- Bottom Rect: $4 \times 2 = 8$.
- Top Rect: Width = $2$ (since total $4$ - right part $2$? No, if left is $2$, top is left part).
- Top Rect sits on left. Width $2$. Height $4$. Area = $8$.
- Total = $8 + 8 = 16$.

- Let's assume the top horizontal width is labeled by the "$4\text{ cm}$" on the right?
- If Top Width = $4\text{ cm}$, then the shape is a rectangle $4$ wide. But the bottom is also $4$ wide. Then it's a rectangle $4 \times 6$. Area $24$. But it's an L-shape.

- Crucial Insight: Look at the position of the "$4\text{ cm}$" label on the right side of Shape 2. It is placed next to the upper vertical segment. The "$2\text{ cm}$" is next to the lower vertical segment.
- Look at the bottom "$4\text{ cm}$".
- Is it possible the inner horizontal width is $4\text{ cm}$? No label there.

- Let's look at Shape 1 again.
- Top widths: $1$ and $3$. Total $4$.
- Left height: $2$. Right height: $3$.
- Areas: $(1\times2) + (3\times3)$? No.
- Left Rect ($1\times2$) + Right Rect ($3\times3$) assumes they are side-by-side from the bottom.
- In Shape 1, the left part is shorter. The right part is taller.
- So, Left Rect: $1\text{ cm}$ wide, $2\text{ cm}$ high. Area $2$.
- Right Rect: $3\text{ cm}$ wide, $3\text{ cm}$ high. Area $9$.
- Total $11$.
- Wait, does the left rect sit on the same baseline? Yes.
- Does the right rect sit on the same baseline? Yes.
- So the total width is $1+3=4$.
- This interpretation works for #1.

- Apply this "Side-by-Side" logic to #2.
- The shape is composed of a Left Rectangle and a Right Rectangle standing side-by-side.
- Left Rectangle: Height is given as $6\text{ cm}$. Width is ???
- Right Rectangle: Height is given as $2\text{ cm}$ (lower label). Width is ???
- We know Total Width (Bottom) = $4\text{ cm}$.
- We know the "step" height is $4\text{ cm}$ (upper right label). This means the Left Rectangle is $4\text{ cm}$ taller than the Right Rectangle. $6 - 2 = 4$. This is consistent.
- We still have two unknowns: Width of Left ($W_L$) and Width of Right ($W_R$).
- We know $W_L + W_R = 4$.
- Is there any other clue?
- Visually, in Shape 2, the left part looks wider than the right part.
- In many such problems, if a dimension is missing, it might be equal to another dimension.
- Could $W_L = 2$ and $W_R = 2$? (Halfway).
- Could $W_L = 3$ and $W_R = 1$?

- Let's look at the label "$4\text{ cm}$" on the right again.
- Is it possible that label refers to the width of the left part?
- Sometimes labels are placed far away.
- If Left Width = $4\text{ cm}$, then Total Width > $4$. But bottom says $4$. Contradiction.

- Let's reconsider the label "$4\text{ cm}$" on the right.
- What if it's not a height? What if it's the width of the top part?
- If Top Width = $4\text{ cm}$, and it's an L-shape where the top part is the left part...
- Then Left Width = $4\text{ cm}$.
- Then Total Width must be at least $4\text{ cm}$.
- The bottom label is $4\text{ cm}$.
- This would imply the Right part has width $0$.

- Is it possible the bottom label "$4\text{ cm}$" is ONLY for the right part?
- If Right Width = $4\text{ cm}$.
- And Left Width is missing?

- Let's try a different perspective.
- Look at Shape 3.
- Left Height $3$, Right Height $4$. Bottom Width $6$. Top-Left Width $2$.
- Here, the "missing" width was calculated: Total ($6$) - Known Part ($2$) = Other Part ($4$).
- Look at Shape 4.
- Top Width $6$, Bottom Width $10$. Left Height $5$, Right Height $2$.
- Here, the "missing" width was calculated: Total ($10$) - Known Part ($6$) = Other Part ($4$).

- Now look at Shape 2.
- We have Total Height ($6$). We have Partial Heights ($4$ and $2$).
- We have Total Width ($4$).
- We have NO Partial Widths.
- This is mathematically unsolvable without an assumption.

- Assumption Check:
- Is it possible the label "$4\text{ cm}$" on the right is actually the width of the top horizontal segment?
- If so, why is it written vertically?
- And if Top Width = $4$, and Bottom Width = $4$, it's a rectangle.

- Is it possible the label "$2\text{ cm}$" on the right is the width of the bottom right segment?
- If Right Width = $2\text{ cm}$.
- Then Left Width = Total ($4$) - Right ($2$) = $2\text{ cm}$.
- Let's test this.
- Left Rect: Width $2$, Height $6$. Area = $12$.
- Right Rect: Width $2$, Height $2$. Area = $4$.
- Total Area = $16$.

- Why would the "$2\text{ cm}$" label be width? It is written vertically next to a vertical line. Unlikely.

- What if the "$4\text{ cm}$" label on the right is the width of the LEFT part?
- If Left Width = $4$, Total Width = $4$, Right Width = $0$. No.

- What if the shape is drawn to scale?
- In Shape 2, the left column looks about twice as wide as the right stub?
- If $W_L = 2 \times W_R$, and $W_L + W_R = 4$.
- $3 W_R = 4 \rightarrow W_R = 1.33$. Unlikely for school math.

- Let's look at the numbers again.
- $6, 4, 2, 4$.
- Maybe the top horizontal width is $2\text{ cm}$?
- If Top Width (Left part) = $2\text{ cm}$.
- Then Right Width = $4 - 2 = 2\text{ cm}$.
- Area = $(2 \times 6) + (2 \times 2) = 12 + 4 = 16$.

- Maybe the top horizontal width is $1\text{ cm}$?
- Area = $(1 \times 6) + (3 \times 2) = 6 + 6 = 12$.

- Let's look at the provided solution for similar worksheets online.
- Often, if a dimension is missing in an L-shape where the other "arm" dimensions are given, there might be a property I'm missing.
- Wait! Look at the label "$4\text{ cm}$" on the right side of Shape 2.
- Look at the label "$4\text{ cm}$" on the bottom.
- Look at the label "$2\text{ cm}$" on the right.
- Look at the label "$6\text{ cm}$" on the left.

- Is it possible the inner horizontal width is intended to be $2\text{ cm}$ because it looks like the height of the bottom part?

- Let's try one more interpretation.
- What if the "$4\text{ cm}$" label on the right is actually labeling the top horizontal edge?
- If Top Edge = $4\text{ cm}$.
- And the shape is a "backward L"? No, it's a standard L.
- If the top edge is $4\text{ cm}$, that's the width of the left column.
- If Left Column Width = $4\text{ cm}$.
- And Bottom Total Width = $4\text{ cm}$.
- Then the right column has width $0$.
- BUT, look at the diagram. The right column clearly exists.
- Therefore, the Bottom Label "$4\text{ cm}$" CANNOT be the total width if the Top Label "$4\text{ cm}$" is the left width.
- OR, the Top Label "$4\text{ cm}$" is NOT the left width.

- Let's assume the question contains a typo and the Bottom Width is meant to be larger, e.g., $6\text{ cm}$?
- If Bottom = $6$, Left Width = $4$ (from right label interpreted as width?), Right Width = $2$.
- Area = $(4 \times 6) + (2 \times 2) = 28$.

- Let's assume the Right Label "$4\text{ cm}$" is Height, and Right Label "$2\text{ cm}$" is Height.
- We are stuck on the width.

- Let's look at the spacing of the text in the image.
- In Shape 1, the gap between the two top numbers is small.
- In Shape 2, there is only one number at the bottom.

- Is it possible that the Left Width is $2\text{ cm}$ and Right Width is $2\text{ cm}$?
- This is the most "standard" integer division of $4$.
- Area = $16$.

- Is it possible that the Left Width is $3\text{ cm}$ and Right Width is $1\text{ cm}$?
- Area = $(3 \times 6) + (1 \times 2) = 20$.

- Let's check the source "WorksheetZone".
- I will bet on the missing dimension being implied by symmetry or equal segments if not stated, OR I am blind to a label.
- Let me zoom in on Shape 2 again.
- Is there a faint label on the top horizontal edge?
- No.
- Is there a label on the inner horizontal edge?
- No.

- Wait! Look at Shape 1.
- Top widths: $1$ and $3$.
- Left height: $2$.
- Right height: $3$.
- The label "$3\text{ cm}$" is on the right vertical edge.
- The label "$2\text{ cm}$" is on the left vertical edge.

- Look at Shape 2.
- Left height: $6$.
- Right heights: $4$ and $2$.
- Bottom width: $4$.

- Look at Shape 3.
- Left height: $3$.
- Right height: $4$.
- Bottom width: $6$.
- Top-left width: $2$.

- Look at Shape 4.
- Top width: $6$.
- Bottom width: $10$.
- Left height: $5$.
- Right height: $2$.

- In Shapes 1, 3, and 4, we have enough info.
- In Shape 2, we do NOT.

- However, there is a common convention in some poorly designed worksheets:
- If the top horizontal edge is not labeled, but the bottom is, and it's an L-shape...
- Maybe the Left Width is equal to the Right Lower Height ($2\text{ cm}$)?
- Maybe the Right Width is equal to the Right Upper Height ($4\text{ cm}$)? No, $2+4=6 \neq 4$.

- Let's try: Left Width = $2\text{ cm}$.
- Why? Because the other vertical segment is $2\text{ cm}$.
- If Left Width = $2$, Right Width = $2$.
- Area = $16$.

- Let's try: Left Width = $4\text{ cm}$ (assuming the bottom label applies to the main block) and the right block is extra?
- If Left Width = $4$, and Right Width is unknown...

- Let's look at the answer key pattern.
- 1) $11$
- 3) $22$
- 4) $38$
- 2) ?

- I will provide the solution based on the most likely intended dimensions: The vertical line dividing the L-shape is in the middle, or the widths are equal ($2$ and $2$), OR the top width is $2$ (matching the bottom height).
- Actually, looking at the visual representation of #2, the left part is significantly wider than the right part.
- If Left Width = $3$ and Right Width = $1$:
- Area = $(3 \times 6) + (1 \times 2) = 20$.
- If Left Width = $2.5$? No.

- Let's reconsider the label "$4\text{ cm}$" on the right.
- What if it is the width of the top part?
- And the bottom label "$4\text{ cm}$" is the width of the bottom part?
- If Top Width = $4$ and Bottom Width = $4$, it is a rectangle.
- BUT, the right side has a cutout.
- This implies the "Bottom Width" label might refer to the Left Part Only?
- If Left Width = $4\text{ cm}$.
- And we need the Right Width.
- Is the Right Width given? No.

- Final Decision Strategy:
- I will note the ambiguity but provide the calculation for the most standard interpretation where a dimension might be shared.
- Actually, look at Shape 1: $1+3=4$.
- Shape 3: $2+4=6$.
- Shape 4: $6+4=10$.
- Shape 2: $? + ? = 4$.
- In Shape 2, the heights are $4$ and $2$.
- Is it possible the widths are also $4$ and $2$?
- If Widths are $4$ and $2$, Total Width = $6$. But label says $4$.
- If Widths are proportional to heights?
- Height Ratio $4:2 = 2:1$.
- Width Ratio $2:1$.
- $W_L + W_R = 4$.
- $2x + x = 4 \rightarrow 3x=4$. No.

- What if the label "$4\text{ cm}$" on the right is the WIDTH of the left part?
- If Left Width = $4$.
- And the bottom label "$4\text{ cm}$" is the TOTAL width.
- Then Right Width = $0$.

- What if the bottom label "$4\text{ cm}$" is the LEFT PART width?
- And the right part width is missing?

- Let's assume the question meant for the Top Horizontal Width to be $2\text{ cm}$.
- This matches the height of the bottom leg.
- Area = $16$.

- Let's assume the question meant for the Left Vertical Width to be $2\text{ cm}$.
- Area = $16$.

- I will go with 16 cm² as the most probable intended answer due to symmetry/equality of the missing dimension with the existing small dimension ($2\text{ cm}$).

3) Shape 3
* Split vertically:
* Left Rectangle: Width is given as $2\text{ cm}$ (top label). Height is given as $3\text{ cm}$ (left label).
* Area = $2 \times 3 = 6\text{ cm}^2$.
* Right Rectangle:
* Height is given as $4\text{ cm}$ (right label).
* Width is Total Width ($6\text{ cm}$) minus Left Width ($2\text{ cm}$) = $4\text{ cm}$.
* Area = $4 \times 4 = 16\text{ cm}^2$.
* Total Area: $6 + 16 = 22\text{ cm}^2$.

4) Shape 4
* Split vertically:
* Left Rectangle: Width is given as $6\text{ cm}$ (top label). Height is given as $5\text{ cm}$ (left label).
* Area = $6 \times 5 = 30\text{ cm}^2$.
* Right Rectangle:
* Height is given as $2\text{ cm}$ (right label).
* Width is Total Width ($10\text{ cm}$) minus Left Width ($6\text{ cm}$) = $4\text{ cm}$.
* Area = $4 \times 2 = 8\text{ cm}^2$.
* Total Area: $30 + 8 = 38\text{ cm}^2$.

Final Answer:
1) 11 cm²
2) 16 cm² (Assuming equal split of width or width matching the smaller height due to missing label)
3) 22 cm²
4) 38 cm²