Calculate area and perimeter of irregular shapes with this educational worksheet featuring six composite figures with labeled dimensions.

Explanation:
We are given six irregular shapes made by combining rectangles. To find the area, we can split each shape into rectangles, compute each rectangle’s area (length × width), and add them up. For perimeter, we trace the outer boundary and add all outer side lengths — be careful not to include internal edges (the dashed lines are just for reference, not part of the perimeter).

Let’s go one shape at a time.

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Shape 1 (top-left, units: cm)
It looks like two rectangles stacked:
- Top rectangle: 4 cm (width) × 2 cm (height) → area = 4 × 2 = 8 cm²
- Bottom rectangle: 3 cm (width) × 4 cm (height) → area = 3 × 4 = 12 cm²
But wait — the bottom rectangle is labeled “4×3” and has width 3 cm, height 4 cm — yes, same as above.
Total area = 8 + 12 = 20 cm²

Now perimeter: Let’s list outer sides clockwise starting from top-left corner:
- Top: 4 cm
- Right side: top part is 2 cm, bottom part is 4 cm → total right = 2 + 4 = 6 cm
- Bottom: 3 cm
- Left side: bottom part is 4 cm, but above that, there’s a 2 cm gap? Wait — look carefully:

The shape has:
- Top rectangle: width 4 cm, height 2 cm
- Below it, a rectangle of width 3 cm, height 4 cm, aligned to the left (so its right side is inset by 1 cm from the top rectangle’s right edge). There's a 1 cm vertical segment on the right side between the two rectangles (that’s the 1 cm shown on the right of the bottom rectangle). So the full outline is:

Start at top-left:
1. Right along top: 4 cm
2. Down right side: 2 cm (top rect height)
3. Right? No — at that point, the bottom rectangle starts 1 cm to the left, so we go down 1 cm (the small vertical gap on the right), then left 1 cm (to align with bottom rect’s right edge), then down 4 cm (bottom rect height), then left 3 cm (bottom width), then up 6 cm (left side total: 2 cm top + 4 cm bottom = 6 cm), back to start.

Wait — better to draw coordinates or use the outer edge method.

Alternative reliable method: Use the “grid” of outer dimensions and subtract missing parts.

But easier: trace the outer boundary step-by-step using given labels:

From diagram:
- Top horizontal: 4 cm
- Right side: from top-right corner down: first 2 cm (top rect), then a 1 cm horizontal step left (the notch), then down 4 cm (bottom rect height) → but that 1 cm horizontal is *internal*? No — the 1 cm labeled on the right side of the bottom rectangle indicates the vertical offset — meaning the bottom rectangle is shifted left by 1 cm relative to the top one.

So outer right edge consists of:
- 2 cm (top rect right side)
- then a horizontal segment left 1 cm (this is part of the outer boundary — it’s a “step”),
- then 4 cm down (right side of bottom rect),
- then bottom: 3 cm left,
- then left side: 6 cm up (since total height is 2 + 4 = 6 cm),
- then top: 4 cm right — but we already did top.

Wait — let’s list vertices in order:

Assume bottom-left corner is at (0,0). Then:
- Bottom rectangle: width 3 cm, height 4 cm → goes from (0,0) to (3,4)
- Top rectangle: width 4 cm, height 2 cm, placed on top of bottom rectangle, aligned left → so its bottom-left is at (0,4), top-right at (4,6)

So coordinates of outer vertices (counterclockwise):
(0,0) → (3,0) → (3,4) → (4,4) → (4,6) → (0,6) → back to (0,0)

Now compute perimeter by summing distances between consecutive points:
- (0,0) to (3,0): 3 cm
- (3,0) to (3,4): 4 cm
- (3,4) to (4,4): 1 cm
- (4,4) to (4,6): 2 cm
- (4,6) to (0,6): 4 cm
- (0,6) to (0,0): 6 cm

Sum: 3 + 4 + 1 + 2 + 4 + 6 = 20 cm

✔ Area = 20 cm², Perimeter = 20 cm

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Shape 2 (top-middle, units: m)
Two rectangles:
- Top: 4 m × 2 m → area = 8 m²
- Bottom: 2 m × 4 m → area = 8 m²
But wait — the bottom rectangle is labeled “4×2”, and placed to the right of a 2 m gap. Actually, from diagram:
Top rectangle: width 4 m, height 2 m
Below it, on the right, a rectangle 2 m wide, 4 m tall, with a 2 m gap on the left.

Coordinates: Let’s set bottom-left of whole shape at (0,0).
Bottom rectangle: from (2,0) to (4,4) → width 2, height 4
Top rectangle: from (0,4) to (4,6) → width 4, height 2

Outer vertices:
(0,0) → (2,0) → (2,4) → (4,4) → (4,6) → (0,6) → (0,0)

Check: Is (0,0) connected directly to (2,0)? Yes — bottom edge of bottom rectangle starts at x=2, so from x=0 to x=2 at y=0 is empty? Wait — no, the shape does not include the left-bottom 2×4 region. So the shape is only the two rectangles — there is a missing 2×4 region on the bottom-left.

So actual shape consists of:
- Top rectangle: x=0 to 4, y=4 to 6
- Bottom rectangle: x=2 to 4, y=0 to 4

So outer boundary vertices (start at (0,4)):
Better: list all outer corners in order:

Start at (0,4) — top-left of top rect
→ (4,4) — top-right of top rect / top-left of bottom rect
→ (4,0) — bottom-right of bottom rect
→ (2,0) — bottom-left of bottom rect
→ (2,4) — top-left of bottom rect (but this is internal? No — from (2,0) to (2,4) is left edge of bottom rect, and from (2,4) to (0,4) is the gap? Wait — (0,4) to (2,4) is the bottom edge of the top rectangle — yes, that’s outer.

So full loop:
(0,4) → (4,4) → (4,0) → (2,0) → (2,4) → (0,4)

That’s a pentagon.

Lengths:
- (0,4) to (4,4): 4 m
- (4,4) to (4,0): 4 m
- (4,0) to (2,0): 2 m
- (2,0) to (2,4): 4 m
- (2,4) to (0,4): 2 m

Sum: 4 + 4 + 2 + 4 + 2 = 16 m

Area: top rect 4×2 = 8, bottom rect 2×4 = 8 → total 16 m²

✔ Area = 16 m², Perimeter = 16 m

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Shape 3 (top-right, units: km)
Top rectangle: 6 km × 2 km → area = 12 km²
Bottom rectangle: 2 km × 3 km → area = 6 km²
But placement: bottom rectangle is centered? From labels: top rect width 6 km, below it a 2×3 rectangle, with 1 km on left and 3 km on right of the bottom rect relative to top rect.

So top rect: x=0 to 6, y=3 to 5 (height 2)
Bottom rect: x=1 to 3, y=0 to 3 (height 3) — because left gap 1 km, width 2 km, then right gap 3 km (1+2+3=6).

Outer vertices:
Start at (0,3) — bottom-left of top rect
→ (6,3) — bottom-right of top rect
→ (6,5) — top-right
→ (0,5) — top-left
→ back? No — need to go down the left side where bottom rect is.

Actually, the shape is like a T upside-down? Wait — diagram shows top rectangle, and below it, a smaller rectangle attached in the middle, so the overall shape has a “notch” on bottom.

Better: list all outer corners:

- Top-left: (0,5)
- Top-right: (6,5)
- Down right side to y=3: (6,3)
- Then right part of bottom is empty; bottom rect starts at x=1, so from (6,3) we go left to x=3 (since bottom rect ends at x=3), but that’s internal? No — the space from x=3 to 6, y=0 to 3 is empty. So outer edge goes:
(6,3) → (6,0)? No, because there’s no material there.

Correct approach: The shape consists of two rectangles that share a side segment? Actually, the dashed line suggests the bottom rectangle is attached under the top one, but offset.

From diagram labels:
- Top rectangle: 6 km long, 2 km high
- Below it, centered? It says left gap 1 km, bottom rect width 2 km, right gap 3 km → so bottom rect spans from x=1 to x=3 (if top is 0–6). Height 3 km downward.

So the shape occupies:
- Region A: 0 ≤ x ≤ 6, 3 ≤ y ≤ 5
- Region B: 1 ≤ x ≤ 3, 0 ≤ y ≤ 3

Outer boundary vertices (counterclockwise):
Start at (0,3) — left end of shared edge? But (0,3) is outer bottom-left corner of top rect, and below it is empty, so (0,3) connects down? No material below x=0 to 1, y=0 to 3, so the left side goes from (0,5) down to (0,3), then horizontally to (1,3), then down to (1,0), then right to (3,0), then up to (3,3), then right to (6,3), then up to (6,5), then left to (0,5).

Yes! That’s correct.

So vertices:
1. (0,5)
2. (6,5)
3. (6,3)
4. (3,3)
5. (3,0)
6. (1,0)
7. (1,3)
8. (0,3)
9. back to (0,5)

Now compute segment lengths:
- (0,5)→(6,5): 6
- (6,5)→(6,3): 2
- (6,3)→(3,3): 3
- (3,3)→(3,0): 3
- (3,0)→(1,0): 2
- (1,0)→(1,3): 3
- (1,3)→(0,3): 1
- (0,3)→(0,5): 2

Sum: 6+2+3+3+2+3+1+2 = 22 km

Area: top = 6×2 = 12, bottom = 2×3 = 6 → total 18 km²

✔ Area = 18 km², Perimeter = 22 km

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Shape 4 (bottom-left, units: cm)
Large rectangle: 5 cm × 6 cm → area = 30 cm²
Minus a small rectangle cut out at bottom-left: 2 cm × 1 cm? Wait — label says “2×1” and width 2 cm, height 1 cm, placed at bottom-left corner, so it's removed.

Actually, the shape is a big rectangle 5 cm (width) × 6 cm (height), with a 2 cm × 1 cm rectangle attached? No — the dashed line and “2×1” suggest a protrusion or indentation.

Looking: The main rectangle is 5 cm wide (top), 6 cm tall (left side). At bottom-left, there’s a small rectangle labeled “2×1”, width 2 cm, height 1 cm, and it's *outside*? The diagram shows it extending leftward from the main rectangle — because the total bottom width is 2 cm (small rect) + 3 cm (main bottom part) = 5 cm, and left side total height is 6 cm, with the small rect height 1 cm.

So coordinates:
- Main rectangle: x=0 to 5, y=0 to 6
- Small rectangle: x=−2 to 0, y=0 to 1 (sticking out left)

Thus outer vertices:
(-2,0) → (0,0) → (5,0) → (5,6) → (0,6) → (0,1) → (-2,1) → (-2,0)

Wait — from (0,6) down to (0,1) is left edge of main rect, but between y=1 and y=0, the left side is the small rect’s right edge at x=0, and the small rect goes to x=−2.

So correct loop:
Start at (-2,0)
→ (5,0) [bottom edge: 2 + 3 = 5]
→ (5,6) [right side]
→ (0,6) [top of main rect]
→ (0,1) [down left side of main rect to where small rect starts]
→ (-2,1) [left edge of small rect]
→ (-2,0) [bottom of small rect]

Segments:
- (-2,0) to (5,0): 7 cm
- (5,0) to (5,6): 6 cm
- (5,6) to (0,6): 5 cm
- (0,6) to (0,1): 5 cm
- (0,1) to (-2,1): 2 cm
- (-2,1) to (-2,0): 1 cm

Sum: 7+6+5+5+2+1 = 26 cm

Area: main rect 5×6 = 30, plus small rect 2×1 = 2 → total 32 cm²

✔ Area = 32 cm², Perimeter = 26 cm

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Shape 5 (bottom-middle, units: m)
Big rectangle: 8 m × 6 m → area = 48 m²
Small rectangle attached at bottom: 6 m × 2 m → but placed centered? Labels: bottom width 6 m, height 2 m, and there’s 2 m on each side (since total bottom width is 8 m, and 8 − 6 = 2 → 1 m each side? Wait — diagram shows: top rectangle 8×6, below it a rectangle 6×2, with 1 m gap on left and 1 m on right? Actually, it says “6x2” and total bottom length is 6 m, and the big rectangle is 8 m wide, so the small rect is centered: 1 m margin left and right.

So shape is like a rectangle with a lower extension centered.

Coordinates:
- Big rect: x=0 to 8, y=2 to 8 (height 6)
- Small rect: x=1 to 7, y=0 to 2 (height 2)

Outer vertices:
(0,2) → (0,8) → (8,8) → (8,2) → (7,2) → (7,0) → (1,0) → (1,2) → back to (0,2)

Segments:
- (0,2)→(0,8): 6
- (0,8)→(8,8): 8
- (8,8)→(8,2): 6
- (8,2)→(7,2): 1
- (7,2)→(7,0): 2
- (7,0)→(1,0): 6
- (1,0)→(1,2): 2
- (1,2)→(0,2): 1

Sum: 6+8+6+1+2+6+2+1 = 32 m

Area: big 8×6 = 48, small 6×2 = 12 → total 60 m²

✔ Area = 60 m², Perimeter = 32 m

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Shape 6 (bottom-right, units: km)
Three rectangles:
- Top square: 10 km × 10 km → area = 100
- Middle rectangle: 10 km × 5 km? Wait — labels: right side shows 15 km total height, top part 10 km, so middle height = 5 km. Width of middle part is 10 km (same as top).
- Bottom rectangle: 20 km × 5 km → area = 100

But layout:
- Top: 10×10 at top-right
- Below it, a 10×5 rectangle (since 15−10=5), same width 10
- To the left of those, a 20×5 rectangle at bottom (height 5), aligned with bottom of middle.

From diagram:
- Total width: 20 km (bottom)
- Top square sits on top of right half: width 10, so left half (10 km) is empty above height 10 km.

Coordinates:
Let’s set origin at bottom-left.
- Bottom rectangle: x=0 to 20, y=0 to 5
- Middle rectangle: x=10 to 20, y=5 to 10
- Top square: x=10 to 20, y=10 to 15

So outer vertices:
(0,0) → (20,0) → (20,5) → (20,10) → (20,15) → (10,15) → (10,10) → (10,5) → (0,5) → (0,0)

Wait — from (10,5) to (0,5) is top of bottom rect, yes.

Now segments:
- (0,0)→(20,0): 20
- (20,0)→(20,5): 5
- (20,5)→(20,10): 5
- (20,10)→(20,15): 5
- (20,15)→(10,15): 10
- (10,15)→(10,10): 5
- (10,10)→(10,5): 5
- (10,5)→(0,5): 10
- (0,5)→(0,0): 5

Sum: 20+5+5+5+10+5+5+10+5 = 70 km

Area:
- Bottom: 20×5 = 100
- Middle: 10×5 = 50
- Top: 10×10 = 100
Total = 250 km²

✔ Area = 250 km², Perimeter = 70 km

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Now compile all:

1. Area = 20 cm², Perimeter = 20 cm
2. Area = 16 m², Perimeter = 16 m
3. Area = 18 km², Perimeter = 22 km
4. Area = 32 cm², Perimeter = 26 cm
5. Area = 60 m², Perimeter = 32 m
6. Area = 250 km², Perimeter = 70 km

Double-check shape 4: main 5×6 = 30, plus 2×1 = 2 → 32, yes. Perimeter we got 26 — let’s verify quickly:
Bottom: 2 (left piece) + 3 (main bottom) = 5? Wait earlier I said 7 cm from -2 to 5 → that’s 7 cm, correct. Left side: from y=0 to y=1 is 1 cm (small rect height), then from y=1 to y=6 is 5 cm (main left side) → total left = 6 cm, but in our path we had (-2,0) to (-2,1): 1 cm, then (-2,1) to (0,1): 2 cm (top of small rect), then (0,1) to (0,6): 5 cm — yes, accounted.

All seem consistent.

Final Answer:
1. Area = 20 cm², Perimeter = 20 cm
2. Area = 16 m², Perimeter = 16 m
3. Area = 18 km², Perimeter = 22 km
4. Area = 32 cm², Perimeter = 26 cm
5. Area = 60 m², Perimeter = 32 m
6. Area = 250 km², Perimeter = 70 km