Math, Grade 6, Surface Area and Volume, Basic & Composite Figures ... - Free Printable

Let’s find the area of this green shape.

We can break it into simpler rectangles, calculate each one’s area, and then add them up.

Looking at the shape, we can split it into 3 parts:

1. The left vertical rectangle
2. The bottom middle rectangle
3. The right big rectangle

But wait — let’s look more carefully. Actually, a better way is to see that the whole shape can be thought of as made from three separate rectangles that don’t overlap:

- Left tall rectangle: width = 3 m, height = ?
Wait — actually, looking at the full height on the right side is 11 m. But the left part doesn’t go all the way down? Let me check the dimensions again.

Actually, let’s try splitting it horizontally or vertically in a smart way.

Alternative approach: Split the shape into 3 non-overlapping rectangles:

Rectangle A (left top):
Width = 3 m
Height = 5.5 m (from top to the inner corner)
→ Area = 3 × 5.5 = 16.5 m²

Rectangle B (bottom middle):
Width = 8 m
Height = 5.5 m (given at bottom)
→ Area = 8 × 5.5 = 44 m²

Rectangle C (right big one):
Width = 8 m
Height = 11 m
→ Area = 8 × 11 = 88 m²

Wait — but if I add these, am I double-counting or missing something?

Actually, no — because Rectangle A is only the top-left protrusion, Rectangle B is the bottom center, and Rectangle C is the entire right block. But notice: the right block (C) already includes the space above the bottom middle part? Hmm, maybe not.

Let me try another method — use the “total bounding box minus cutouts” idea? Or just trace the outline.

Better yet — let’s divide the shape into 3 clear rectangles that together make the whole thing without overlapping:

Option: Divide vertically.

Left column:
It has two parts? Actually, the leftmost part is 3m wide, and its total height is... from top to bottom? The bottom of the left part aligns with the bottom of the middle bottom rectangle? Let’s see:

From the diagram:

- The left vertical strip is 3m wide.
- From top to the inner horizontal line: 5.5m
- Then below that, there’s a gap until the bottom? No — actually, the left part goes all the way down? Wait, no — look at the bottom: there’s a 5.5m segment on the left bottom, which is under the left vertical part? This is confusing.

Let me label points mentally.

Start from top-left corner.

Go right 3m → then down 5.5m → then right 8m → then up to meet the top of the right block? No.

Actually, here’s a better plan: Use the fact that the entire figure can be divided into 3 rectangles:

1. Top-left rectangle: 3m (width) × 5.5m (height) = 16.5 m²

2. Bottom-middle rectangle: 8m (width) × 5.5m (height) = 44 m²

3. Right rectangle: This one is tricky. Its width is 8m, and its height is 11m, BUT — does it include the area that’s already covered by the bottom-middle? No, because the bottom-middle is centered? Wait, let’s check alignment.

Actually, looking at the bottom: the bottom-middle rectangle is 8m wide, and on its left and right, there are 5.5m segments going up? No — the labels say:

At the bottom: left side has "5.5 m" pointing to the vertical drop, and same on right. And the bottom edge of the middle part is labeled "8 m".

Also, on the right side, the full height is 11m.

Now, the key: the right rectangle (8m wide, 11m high) sits such that its bottom is aligned with the bottom of the entire shape? Yes, because the 5.5m on the right bottom is the vertical distance from the bottom of the right rectangle up to where the middle bottom rectangle starts? Actually, no — let's think differently.

I think the safest way is to consider the entire shape as composed of:

- A large rectangle on the right: 8m wide × 11m high = 88 m²

- Plus a rectangle on the bottom middle: 8m wide × 5.5m high = 44 m² — but wait, this would overlap with the right rectangle if they share space.

No — actually, the bottom middle rectangle is attached to the bottom of the right rectangle? Not exactly.

Let me sketch mentally:

The right part is a solid 8x11 rectangle.

Attached to its left side, at the bottom, is an 8m wide by 5.5m high rectangle — but that would extend leftward, and since the right rectangle is 8m wide, adding an 8m wide rectangle to its left would make the total width 16m at the bottom, but the diagram shows that on the left of the bottom middle, there's a 5.5m vertical segment, meaning the bottom middle rectangle is not flush with the left edge of the right rectangle.

This is getting messy. Let's use coordinates.

Set origin at bottom-left corner of the entire shape.

From the diagram:

- The bottom-left corner: let's call it (0,0)

- Moving right along bottom: first 5.5m is vertical? No, the label "5.5 m" on the bottom left is likely the height of the left-bottom part.

Actually, re-examining the image description:

The shape has:

- On the far left: a vertical segment of 3m at the top, then down 5.5m, then right 8m, then up to connect to the right block.

Perhaps it's easier to calculate the area by dividing into three parts that are clearly defined:

Part 1: The left tower — 3m wide, and how tall? From top to the level where it meets the middle horizontal part. That height is 5.5m + the height of the bottom part? No.

Notice that the total height on the right is 11m. The bottom part has a height of 5.5m (as labeled on the sides). So the upper part on the right must be 11 - 5.5 = 5.5m high? But the right block is drawn as a single rectangle.

Another idea: The shape can be seen as a combination of:

- A rectangle on the left: 3m wide × (5.5m + 5.5m) = 3 × 11 = 33 m²? Is that correct?

Let's see: if the left part goes from top to bottom, its height should be the same as the right part's height, which is 11m. But is it? Looking at the diagram, the left part has a "step" — it goes down 5.5m, then right 8m, so the left part's total height is not 11m; it's only 5.5m for the top part, and then below that, there's the bottom middle part.

I think I found a reliable way:

Divide the shape into 3 rectangles:

1. Top-left rectangle: width 3m, height 5.5m → area = 3 * 5.5 = 16.5 m²

2. Bottom rectangle: this spans the entire bottom width. What is the total width at the bottom?

From left to right at the bottom:

- Left overhang: 5.5m (vertical label, but that's height; the horizontal extent?)

Actually, the bottom consists of:

- A left section: from x=0 to x=a, but we need to infer.

From the diagram, the bottom-middle rectangle is 8m wide, and on its left, there is a 5.5m vertical segment, which means that the left part of the bottom is indented.

Perhaps the total width of the shape at the bottom is: left indent + middle + right indent.

The labels show:

- At the bottom, on the left, "5.5 m" is written next to a vertical line, indicating the height of the left-bottom part is 5.5m, and similarly on the right.

And the bottom edge of the middle part is 8m.

Also, the top has: left 3m, then after the step, 8m to the right block, and the right block is 8m wide.

So, let's calculate the total width.

From left to right:

- The leftmost part is 3m wide (top).

- Then there is a recess of 8m wide (the horizontal part at the top-middle).

- Then the right block is 8m wide.

But the right block extends down, and at the bottom, the middle part is 8m wide, with 5.5m on each side vertically.

To avoid confusion, let's use the following division:

Rectangle 1: The entire right block — 8m wide × 11m high = 88 m²

Rectangle 2: The bottom-middle extension — but this is already included in the right block? No.

Actually, the bottom-middle rectangle is separate and to the left of the right block.

Let me define:

- Rectangle A: left-top: 3m (w) × 5.5m (h) = 16.5 m²

- Rectangle B: the central horizontal part at the top? No.

Another standard method for such shapes is to use the "additive" approach with non-overlapping regions.

Let me try this:

The shape can be divided into:

1. A rectangle on the left: 3m wide, and its height is from y=5.5m to y=11m? Let's set y=0 at the bottom.

Assume the bottom of the shape is at y=0.

Then:

- The bottom-middle rectangle: from y=0 to y=5.5m, and from x= ? to x= ?

From the diagram, the bottom-middle rectangle is 8m wide, and it is centered or positioned such that on its left, there is a vertical rise of 5.5m, and on its right, also 5.5m.

Also, the right block is 8m wide and 11m high, so it occupies from y=0 to y=11m, and from x= c to x=c+8.

Similarly, the left part: at the top, from y=5.5m to y=11m, x=0 to x=3m.

Then, between x=3m and x=3+8=11m, at y=5.5m to y=11m, there is a gap? No, because the right block starts at some x.

Let's calculate the position.

Suppose the right block starts at x = d.

Then, the bottom-middle rectangle is from x = e to x=e+8, at y=0 to y=5.5m.

From the diagram, the distance from the left edge of the bottom-middle to the left edge of the right block is 5.5m? The label "5.5 m" on the right bottom is likely the horizontal distance or vertical? In the image, it's placed next to a vertical line, so it's probably the height of the vertical segment.

In standard interpretation, when a dimension is placed next to a vertical line, it indicates the length of that vertical line, i.e., height.

So, on the bottom left, there is a vertical segment of height 5.5m, which means that from the bottom (y=0) up to y=5.5m, there is a wall, and then it turns right.

Similarly on the right.

For the bottom-middle rectangle, it is at y=0 to y=5.5m, and its width is 8m.

Now, what is its x-position? It must be that the left end of this rectangle is at x = a, and the right end at x=a+8.

Then, to the left of it, from x=0 to x=a, there is the left part, which at y=0 to y=5.5m is empty? No, because the left part has a vertical segment at x=0 from y=5.5m to y=11m, and at y=0 to y=5.5m, there might be nothing, but the diagram shows a connection.

Actually, looking back, the left part is only the top-left 3x5.5, and then below that, from y=0 to y=5.5m, the shape extends from x=0 to x=3m? But the label "5.5 m" on the bottom left suggests that there is a vertical side of 5.5m, which would be from y=0 to y=5.5m at x=0.

I think I have it:

The shape has:

- From x=0 to x=3m: this column exists from y=5.5m to y=11m (top-left rectangle) AND from y=0 to y=5.5m (bottom-left rectangle)? But the diagram doesn't show that; it shows a step.

Upon second thought, in the diagram, the left part is only the top 3m wide by 5.5m high, and then below that, the shape moves right, so at y<5.5m, the left part is not present; instead, the bottom-middle rectangle starts.

But then how is the left side connected? There must be a vertical segment on the left from y=0 to y=5.5m.

Yes! The "5.5 m" label on the bottom left is for the vertical side from (0,0) to (0,5.5), and then from (0,5.5) to (3,5.5) is the bottom of the top-left rectangle, but that would mean the top-left rectangle is from y=5.5 to y=11, x=0 to x=3.

Then from (3,5.5) to (3+8=11,5.5) is the top of the bottom-middle rectangle? No.

Let's list the vertices.

Start at (0,0) — bottom-left corner.

Move up 5.5m to (0,5.5) — this is the left-bottom vertical.

Then move right 3m to (3,5.5) — this is the bottom of the top-left rectangle.

Then move up 5.5m to (3,11) — top of left part.

Then move right 8m to (11,11) — but the right block is 8m wide, so if it starts at x=11, then it goes to x=19, but that seems too wide.

The right block is labeled 8m wide, and the top has "8 m" for the right block, and "3 m" for the left, and "8 m" for the middle top.

So from left to right at the top: 3m (left) + 8m (middle gap) + 8m (right) = 19m total width at top.

At the bottom, the bottom-middle rectangle is 8m wide, and on its left and right, there are vertical segments of 5.5m, which likely mean that the bottom-middle rectangle is inset.

Specifically, the total width at the bottom is: left indent + 8m + right indent.

What is the left indent? From the left edge to the start of the bottom-middle rectangle.

From the diagram, the left edge at bottom is at x=0, and the bottom-middle rectangle starts at x=5.5m? Because the "5.5 m" on the bottom left is probably the horizontal distance, but it's placed next to a vertical line, so it's ambiguous.

In many such problems, when a dimension is placed next to a vertical line, it is the length of that line, i.e., height.

So, the vertical line on the bottom left has length 5.5m, so from y=0 to y=5.5m at x=0.

Then, from (0,5.5) to (3,5.5) is a horizontal line (bottom of top-left rectangle).

Then from (3,5.5) to (3,11) is vertical (right side of top-left rectangle).

Then from (3,11) to (3+8=11,11) is horizontal (top of the middle gap).

Then from (11,11) to (11,11- something) — but the right block is 8m wide, so if it starts at x=11, it goes to x=19, and down to y=0.

But then the bottom-middle rectangle: it is 8m wide, and at y=0 to y=5.5m, and it must be between x=5.5 and x=13.5 or something.

This is inconsistent.

Let's look for symmetry or use the given numbers.

Notice that the right block is 8m wide and 11m high.

The bottom-middle rectangle is 8m wide and 5.5m high.

The top-left rectangle is 3m wide and 5.5m high.

Now, are these three rectangles disjoint? Let's see their positions.

Assume the right block occupies x from P to P+8, y from 0 to 11.

The bottom-middle rectangle occupies x from Q to Q+8, y from 0 to 5.5.

The top-left rectangle occupies x from 0 to 3, y from 5.5 to 11.

For them to be connected and form the shape, likely:

- The top-left rectangle is at x=0 to 3, y=5.5 to 11.

- The right block is at x= R to R+8, y=0 to 11.

- The bottom-middle rectangle is at x= S to S+8, y=0 to 5.5.

From the diagram, the distance between the top-left and the right block is 8m horizontally at y=11, so from x=3 to x=3+8=11, so the right block starts at x=11.

So right block: x=11 to 19, y=0 to 11.

Then, the bottom-middle rectangle: it is 8m wide, and it is below the gap, so probably from x=3 to x=11, y=0 to 5.5? But then its width is 8m, from 3 to 11 is 8m, yes.

And on the left, from x=0 to x=3, at y=0 to 5.5, is there anything? The diagram shows a vertical segment at x=0 from y=0 to y=5.5, so yes, there is a rectangle from x=0 to 3, y=0 to 5.5.

Oh! I missed that.

So actually, there are four rectangles:

1. Bottom-left: x=0 to 3, y=0 to 5.5 → area = 3 * 5.5 = 16.5 m²

2. Top-left: x=0 to 3, y=5.5 to 11 → area = 3 * 5.5 = 16.5 m²

3. Bottom-middle: x=3 to 11, y=0 to 5.5 → area = 8 * 5.5 = 44 m²

4. Right block: x=11 to 19, y=0 to 11 → area = 8 * 11 = 88 m²

But is the right block from x=11 to 19? And the bottom-middle from x=3 to 11, so at y=0 to 5.5, from x=3 to 11 is covered, and from x=11 to 19 is the right block, so no overlap.

At y=5.5 to 11, from x=0 to 3 is top-left, from x=3 to 11 is empty? But in the diagram, between x=3 and x=11 at y>5.5, there is the "8 m" label at the top, which is the gap, so yes, it's empty.

Then the right block is from x=11 to 19, y=0 to 11.

But what about the connection? At y=5.5, from x=3 to 11, it's the top of the bottom-middle rectangle, and above it is air, and the right block starts at x=11, so at x=11, y=0 to 11, it's solid.

Now, is there a rectangle at x=3 to 11, y=5.5 to 11? No, because that's the gap.

So the shape consists of:

- Left column: x=0 to 3, y=0 to 11 → this is two rectangles stacked: bottom-left and top-left, total area 3*11 = 33 m²

- Bottom-middle: x=3 to 11, y=0 to 5.5 → 8*5.5 = 44 m²

- Right block: x=11 to 19, y=0 to 11 → 8*11 = 88 m²

But is the left column continuous? Yes, from y=0 to 11 at x=0 to 3.

In the diagram, is there a vertical line at x=3 from y=0 to 11? The diagram shows that at x=3, from y=0 to 5.5, it's the right side of the bottom-left, and from y=5.5 to 11, it's the right side of the top-left, so yes, it's continuous.

Then from x=3 to 11, only from y=0 to 5.5 is filled (bottom-middle), and from y=5.5 to 11 is empty.

Then from x=11 to 19, y=0 to 11 is filled (right block).

Now, check the widths:

At the top (y=11): from x=0 to 3 (left), then x=3 to 11 empty, then x=11 to 19 (right) — so the top has segments at 0-3 and 11-19, with gap 3-11, which matches the "3 m" and "8 m" labels (since 11-3=8m gap).

At the bottom (y=0): from x=0 to 3 (left), x=3 to 11 (bottom-middle), x=11 to 19 (right) — so continuous from 0 to 19, but the diagram shows that at the bottom, there are "5.5 m" labels on the sides, which might indicate the height of the vertical parts, but in this case, at x=0, from y=0 to 5.5 is part of the left column, and from y=5.5 to 11 is also part, so the vertical side at x=0 is 11m high, but the label says "5.5 m" — contradiction.

Ah, here's the issue: in the diagram, the "5.5 m" on the bottom left is likely not the height of the entire left side, but only the lower part.

Perhaps the left column is not full height.

Let's read the diagram again.

Typically in such diagrams, the dimensions are placed to indicate the length of the adjacent side.

So, on the left side, at the bottom, there is a vertical line segment labeled "5.5 m", which means that segment is 5.5m long, so from y=0 to y=5.5 at x=0.

Then, at the top, there is a horizontal segment labeled "3 m" at the very top left.

Then, from the end of that, down 5.5m (labeled), then right 8m (labeled), then up to the top of the right block.

The right block has top labeled "8 m", and right side labeled "11 m".

Also, at the bottom, on the right, "5.5 m" labeled next to a vertical line.

And at the bottom, the middle part has "8 m" for its width.

So, let's define the vertices in order.

Start at bottom-left corner: point A(0,0)

Move up 5.5m to B(0,5.5) [vertical, labeled 5.5m]

Move right 3m to C(3,5.5) [horizontal, but not labeled; however, the top-left is 3m wide, so likely]

From C(3,5.5) move up 5.5m to D(3,11) [vertical, labeled 5.5m on the left side? The label "5.5 m" is on the left, but for the segment from B to C? No, the label "5.5 m" is next to the vertical from A to B, and another "5.5 m" is next to the vertical from C to D? In the image, there is "5.5 m" on the left side between the bottom and the step, and another "5.5 m" on the left side above the step? Let's assume.

From the user's image description, there is "5.5 m" on the left side, which is probably for the lower vertical, and "5.5 m" on the top-left vertical? But in the text, it's listed as "5.5 m" near the top-left vertical.

To resolve, let's count the areas based on common practice.

I recall that for such shapes, a good way is to calculate the area as the sum of the areas of the rectangles that make it up, ensuring no overlap.

Let me try this division:

- Rectangle 1: the left part including both top and bottom: but it's not a single rectangle.

Notice that the shape can be seen as:

- A large rectangle of width W and height H, minus some parts, but it's irregular.

Another idea: use the grid or calculate by parts.

Let's list all the rectangular regions that are filled:

1. The region from x=0 to x=3, y=5.5 to y=11: area = 3 * 5.5 = 16.5 m²

2. The region from x=0 to x=3, y=0 to y=5.5: area = 3 * 5.5 = 16.5 m² -- but is this present? In the diagram, if there is a vertical segment at x=0 from y=0 to y=5.5, and then from (0,5.5) to (3,5.5), and then up, then yes, this region is filled.

3. The region from x=3 to x=11, y=0 to y=5.5: area = 8 * 5.5 = 44 m² (since 11-3=8)

4. The region from x=11 to x=19, y=0 to y=11: area = 8 * 11 = 88 m² (assuming the right block is 8m wide)

But then the total width at bottom is 19m, and at top, from x=0 to 3 and x=11 to 19, so gap from 3 to 11, which is 8m, matching the "8 m" label at the top middle.

Now, the only thing is the "5.5 m" labels on the bottom sides. In this configuration, at x=0, the vertical side from y=0 to y=11 is 11m, but the label says "5.5 m" for the bottom part. Perhaps the "5.5 m" on the bottom left is for the segment from y=0 to y=5.5, which is correct, and there is another "5.5 m" for the segment from y=5.5 to y=11, which is also 5.5m, so it's consistent if we interpret that the left side has two segments of 5.5m each.

In the diagram, there is "5.5 m" written on the left side, and it might be intended for the lower part, and the upper part is also 5.5m, but not labeled separately, or perhaps it is labeled.

In the user's input, it says: "5.5 m" appears twice on the left: once near the top-left vertical, and once near the bottom-left vertical? Let's see the text: "5.5 m" is listed, and in the image, likely there are two "5.5 m" on the left side.

Upon checking the initial problem: "5.5 m" is mentioned, and in the context, probably there is a "5.5 m" for the vertical from bottom to the step, and another "5.5 m" for the vertical from the step to the top on the left.

Similarly on the right, "5.5 m" for the bottom vertical.

In my current division, with four rectangles:

- Bottom-left: 3x5.5 = 16.5

- Top-left: 3x5.5 = 16.5

- Bottom-middle: 8x5.5 = 44

- Right: 8x11 = 88

Sum = 16.5 + 16.5 + 44 + 88 = let's calculate: 16.5+16.5=33, 33+44=77, 77+88=165 m²

But is the right block really 8x11? And is it from x=11 to 19? Then the bottom-middle is from x=3 to 11, so at x=11, it is shared, but since it's a line, area is fine.

However, in the right block, from y=0 to 11, but the bottom-middle is only up to y=5.5, so no overlap.

Now, check the right side: at x=19, y=0 to 11, vertical side 11m, labeled "11 m", good.

At the bottom right, there is a "5.5 m" label next to a vertical line. In this case, at x=19, from y=0 to y=5.5, is there a separate segment? No, it's part of the right block. But the label "5.5 m" on the bottom right might be for the vertical from y=0 to y=5.5 at the right edge of the bottom-middle or something.

Perhaps the "5.5 m" on the bottom right is for the vertical segment from the bottom to the start of the right block, but in this case, the right block starts at y=0.

I think there's a mistake.

Let's look for a different division.

Notice that the right block is 8m wide and 11m high, but it may not start at x=11.

From the top: the left part is 3m wide, then a gap of 8m, then the right block 8m wide, so the right block starts at x=3+8=11, as before.

At the bottom, the bottom-middle rectangle is 8m wide, and it is located such that its left end is at x=5.5m or something.

The "5.5 m" on the bottom left is likely the horizontal distance from the left edge to the start of the bottom-middle rectangle.

In many diagrams, when a dimension is placed at the bottom next to a vertical line, it could be the offset.

Assume that the "5.5 m" on the bottom left is the x-distance from x=0 to the start of the bottom-middle rectangle.

Similarly on the right.

So, let's say:

- The bottom-middle rectangle starts at x=5.5m, ends at x=5.5+8=13.5m, at y=0 to y=5.5m.

- The left part: from x=0 to x=3m, but at what y? From y=5.5m to y=11m for the top-left, and from y=0 to y=5.5m for the bottom-left? But then at x=0 to 3, y=0 to 5.5, it would be filled, but the bottom-middle starts at x=5.5, so from x=3 to 5.5, at y=0 to 5.5, is it filled or not?

This is complicated.

Perhaps the shape is symmetric or has specific properties.

Another approach: calculate the area by considering the bounding box and subtracting the cutouts, but it's easier to add the parts.

Let's consider the following three rectangles that cover the shape without overlap:

1. The left vertical rectangle: width 3m, height 11m (from y=0 to y=11) — area = 3*11 = 33 m²

2. The bottom horizontal rectangle: width 8m, height 5.5m, but positioned from x=3 to x=11, y=0 to y=5.5 — area = 8*5.5 = 44 m²

3. The right vertical rectangle: width 8m, height 11m, from x=11 to x=19, y=0 to y=11 — area = 8*11 = 88 m²

But then the left vertical rectangle includes from x=0 to 3, y=0 to 11, which includes the area that might be overlapped with the bottom horizontal if it were at x=0 to 3, but in this case, the bottom horizontal is at x=3 to 11, so no overlap with left vertical.

At x=3, it's a line, so ok.

Now, is the region from x=3 to 11, y=0 to 5.5 covered by the bottom horizontal, and from x=0 to 3, y=0 to 11 by left vertical, and x=11 to 19, y=0 to 11 by right vertical.

Then the only missing part is whether the top-left is included, which it is in the left vertical.

But in this case, the left vertical is 3x11=33, which includes both the bottom-left and top-left.

Then bottom-middle 8x5.5=44, right 8x11=88.

Sum 33+44+88=165 m².

Now, check the "5.5 m" labels.

On the left side, the vertical side from y=0 to y=11 is 11m, but the diagram has "5.5 m" labeled, which might be for half of it, or perhaps it's labeled for the lower part.

In the user's input, it says "5.5 m" is written, and in the image, likely there is a "5.5 m" for the segment from y=0 to y=5.5 on the left, and another "5.5 m" for y=5.5 to y=11 on the left, so together 11m, so it's consistent.

Similarly, on the right, "5.5 m" for the bottom part, but in this case, the right block is full 11m, so the "5.5 m" on the bottom right might be for the vertical from y=0 to y=5.5 at the right edge of the bottom-middle or something.

Perhaps for the right side, the "5.5 m" is for the vertical segment from y=0 to y=5.5 at x=13.5 or whatever.

To verify, let's calculate the area using another method.

Consider the shape as a combination of:

- A rectangle of width 3+8+8=19m and height 5.5m for the bottom part, but then the top has additional parts.

At y=0 to y=5.5, the shape extends from x=0 to x=19? In my earlier assumption, from x=0 to 3 (left), x=3 to 11 (bottom-middle), x=11 to 19 (right), so yes, from x=0 to 19 at y=0 to 5.5, so area = 19 * 5.5 = 104.5 m²

Then at y=5.5 to y=11, the shape has: from x=0 to 3 (top-left), and from x=11 to 19 (right block), so width 3 + 8 = 11m, height 5.5m, area = 11 * 5.5 = 60.5 m²

Total area = 104.5 + 60.5 = 165 m²

Same as before.

Now, check the labels:

- At the top: left 3m, then gap 8m (from x=3 to 11), then right 8m (x=11 to 19), good.

- On the left side: from y=0 to y=5.5, vertical segment at x=0, length 5.5m, labeled "5.5 m" — good.

From y=5.5 to y=11, vertical segment at x=0, length 5.5m, and if there is a "5.5 m" label for that, good.

- On the right side: from y=0 to y=11, vertical at x=19, length 11m, labeled "11 m" — good.

But the diagram also has "5.5 m" on the bottom right. In this configuration, at the bottom right, at x=19, y=0 to 5.5, it is part of the right block, but the "5.5 m" might be intended for the vertical segment at the right edge of the bottom-middle rectangle.

In the bottom, the bottom-middle rectangle ends at x=11, and the right block starts at x=11, so at x=11, from y=0 to y=5.5, it is the boundary.

The "5.5 m" on the bottom right might be for the vertical from y=0 to y=5.5 at x=13.5 or something, but in our case, it's not necessary.

Perhaps the "5.5 m" on the bottom right is for the horizontal distance or something else.

Another possibility: in some interpretations, the "5.5 m" on the bottom right is the height of the vertical segment from the bottom to the level where the right block starts, but in this case, it starts at y=0.

I think 165 m² is correct, and the labels are consistent if we assume that the left side has two 5.5m segments, and the right side has the full 11m, and the "5.5 m" on the bottom right might be a misplacement or for the bottom-middle's right side, but since it's internal, it's not labeled.

Perhaps for the right side, the "5.5 m" is for the vertical from y=0 to y=5.5 at the left edge of the right block, but that would be at x=11, and it's internal.

To confirm, let's see if there is a standard way.

I recall that in such problems, the area is often calculated as the sum of the areas of the constituent rectangles.

Moreover, 165 m² is a nice number.

Let's calculate numerically:

3 * 5.5 = 16.5

3 * 5.5 = 16.5 (for left column)

8 * 5.5 = 44 (bottom-middle)

8 * 11 = 88 (right)

Sum: 16.5 + 16.5 = 33; 33 + 44 = 77; 77 + 88 = 165

Or as I did later: bottom strip 19*5.5 = 104.5, top strip 11*5.5 = 60.5, sum 165.

Now, 19*5.5: 19*5 = 95, 19*0.5=9.5, total 104.5

11*5.5 = 60.5

104.5 + 60.5 = 165

Yes.

And the dimensions match: total width at bottom 19m, at top 3+8+8=19m, but with gap in middle at top.

Height 11m.

So I think it's correct.

Therefore, the area is 165 square meters.

Final Answer: 165