Find the area and perimeter of each composite figure in this math worksheet.

Let's solve each composite figure step by step. We will find the area and perimeter of each shape.

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1) Figure 1

Given:
- A composite figure made of two rectangles.
- Dimensions:
- Top rectangle: 10 cm (length), 3 cm (height)
- Bottom rectangle: 5 cm (width), 4 cm (height)
- Total height on right side = 7 cm → So bottom part is 7 - 3 = 4 cm tall

We can split this into two rectangles:

#### Rectangle A (top):
- Length = 10 cm
- Height = 3 cm
- Area = 10 × 3 = 30 cm²

#### Rectangle B (bottom):
- Width = 5 cm
- Height = 4 cm
- Area = 5 × 4 = 20 cm²

> But wait — we must ensure no overlap and correct dimensions.

Actually, the total width at the bottom is 5 cm, but the top is 10 cm. So the left side has a 5 cm projection downward from the top.

So better to think:
- The full figure can be divided into:
- Left rectangle: 5 cm wide × (3 + 4) = 5 × 7 = 35 cm²
- Right rectangle: (10 - 5) = 5 cm wide × 4 cm high = 5 × 4 = 20 cm²

Wait — that’s not right either. Let's look carefully.

From the diagram:
- The top is 10 cm wide and 3 cm high.
- Then below it, on the right, there's a rectangle of 5 cm wide and 4 cm high.
- So the left portion extends down 3 cm, then continues down 4 cm?

Actually, let's label:

The figure has:
- A horizontal top of 10 cm
- A vertical drop on the left side of 3 cm
- Then a step down in the middle
- On the right, total height is 7 cm → so the lower part is 4 cm high
- The base is 5 cm wide

So, the shape is like a "U" flipped upside down? No, more like a rectangle with a notch on the bottom-left?

Wait — actually, it's a rectangle missing a smaller rectangle from the bottom-left corner?

No — let's analyze:

Looking at the labels:
- Top: 10 cm
- Left side: 3 cm (top portion), then a 4 cm segment below?
- But the right side is 7 cm → so total height is 7 cm
- Bottom base is 5 cm

So likely:
- The top rectangle is 10 cm wide × 3 cm high
- Below it, on the right, a rectangle of 5 cm wide × 4 cm high
- So the gap on the left is 10 - 5 = 5 cm wide, and 4 cm high? But no — the bottom is only 5 cm wide.

Wait — perhaps the figure is composed of:
- A large rectangle: 10 cm × 7 cm → area = 70 cm²
- Minus a small rectangle removed from the bottom-left: 5 cm wide × 4 cm high? But that doesn't make sense because the bottom is only 5 cm.

Alternative approach: divide into two rectangles.

Let’s do this:

Split the figure into two parts:

#### Part 1: Top rectangle
- Width = 10 cm
- Height = 3 cm
- Area = 10 × 3 = 30 cm²

#### Part 2: Bottom rectangle
- Width = 5 cm
- Height = 4 cm
- Area = 5 × 4 = 20 cm²

But are these adjacent? Yes — the top rectangle covers the full width, and the bottom one sits under the right side.

So total area = 30 + 20 = 50 cm²

Now, perimeter:

Add all outer edges:

Start from top-left:
- Top: 10 cm
- Right side: 7 cm (full height)
- Bottom: 5 cm
- Left side: 4 cm (bottom part) + 3 cm (top part)? Wait — the left side has a step.

Let’s trace the perimeter:

- Top: 10 cm → right
- Down right side: 7 cm → down
- Bottom: 5 cm → left
- Up the inner left side: 4 cm → up
- Then left along the top of the "notch": 5 cm → left
- Then up the outer left side: 3 cm → up

Wait — let’s go clockwise:

Start at top-left corner:
1. Right along top: 10 cm
2. Down right side: 7 cm
3. Left along bottom: 5 cm
4. Up inner vertical: 4 cm (this is the inside edge of the step)
5. Left along the horizontal step: 5 cm (from x=5 to x=0 at y=3)
6. Up the outer left side: 3 cm

Total perimeter = 10 + 7 + 5 + 4 + 5 + 3 = 34 cm

Wait — but the step creates an extra edge.

Let me draw mentally:

- Top: 10 cm
- Right: 7 cm
- Bottom: 5 cm
- Then up a vertical line of 4 cm (on the inside)
- Then left a horizontal line of 5 cm (at height 3 cm)
- Then up the outer left side: 3 cm

Yes — so the perimeter includes:
- Top: 10
- Right: 7
- Bottom: 5
- Inner vertical: 4
- Inner horizontal: 5
- Outer left: 3

But wait — the inner horizontal is 5 cm (from x=5 to x=0 at y=3), and the outer left is 3 cm.

So total = 10 + 7 + 5 + 4 + 5 + 3 = 34 cm

✔

But check: is the left side continuous? No — it has a step.

So yes, the outer boundary is:
- Top: 10
- Right: 7
- Bottom: 5
- Inner vertical: 4
- Inner horizontal: 5
- Outer vertical: 3

Sum: 10+7+5+4+5+3 = 34 cm

So:

Area: 30 + 20 = 50 cm²
Perimeter: 34 cm

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2) Figure 2

Dimensions:
- Overall width: 10 mm
- Overall height: 8 mm
- But a notch on the top-right
- Top horizontal segment: 6 mm
- Right side: 6 mm (so the notch goes down 2 mm from top)

So:
- The main rectangle is 10 mm × 8 mm → area = 80 mm²
- But a smaller rectangle is missing from the top-right corner?

Wait — the figure has a step on the top-right.

Looking:
- Top: 6 mm → then a drop down 2 mm → then continue right
- Right side: 6 mm → so the bottom is 10 mm wide, top is shorter

So it's like a rectangle with a notch cut out from the top-right

But the top is only 6 mm long, then drops down 2 mm, then continues horizontally for the rest.

So we can divide into two rectangles:

#### Rectangle A (bottom):
- Width = 10 mm
- Height = 6 mm
- Area = 10 × 6 = 60 mm²

#### Rectangle B (top):
- Width = 6 mm
- Height = 2 mm (since total height is 8 mm, bottom is 6 mm)
- Area = 6 × 2 = 12 mm²

Total area = 60 + 12 = 72 mm²

Now perimeter:

Trace the outer edge:

Start at bottom-left:
1. Right: 10 mm
2. Up right side: 8 mm
3. Left along top: 6 mm
4. Down vertical step: 2 mm
5. Left along the top of the step: 4 mm (since 10 - 6 = 4)
6. Down the left side: 6 mm

Wait — let's go step by step:

- Bottom: 10 mm → right
- Up right side: 8 mm → up
- Left along top: 6 mm → left
- Down vertical: 2 mm → down (this is the step)
- Left along horizontal: 4 mm → left (from x=6 to x=2? Wait — no)

Wait — after going left 6 mm from right end, we're at x=4 (since total width 10), so we go down 2 mm to the level where the top of the lower rectangle starts.

Then we go left along the top of the lower rectangle? No — the top of the lower rectangle is at height 6 mm, and the step is at height 6 mm.

Wait — the step is inward, so the top of the figure is:
- From left to x=6: 8 mm high
- Then from x=6 to x=10: only 6 mm high

So the top edge is:
- Left part: 6 mm wide at height 8 mm
- Then a vertical drop of 2 mm at x=6
- Then horizontal to x=10 at height 6 mm

So perimeter:

Start at bottom-left:
1. Right: 10 mm → to bottom-right
2. Up: 6 mm → to the step level (y=6)
3. Left: 4 mm → to x=6 at y=6
4. Up: 2 mm → to y=8 at x=6
5. Left: 6 mm → to x=0 at y=8
6. Down: 8 mm → back to start

Wait — no:

After step 4: up 2 mm → to (6,8)
Then left 6 mm → to (0,8)
Then down 8 mm → to (0,0)

But we already went from (0,0) to (10,0), so now we're closing.

So list:
- Bottom: 10 mm
- Up right side: 6 mm (to y=6)
- Left: 4 mm (to x=6 at y=6)
- Up: 2 mm (to y=8)
- Left: 6 mm (to x=0)
- Down: 8 mm (back to start)

Total = 10 + 6 + 4 + 2 + 6 + 8 = 36 mm

But wait — the left side is 8 mm, and the top is 6 mm, but the step adds extra edges.

Yes — so perimeter is:
- Bottom: 10
- Right: 6
- Step horizontal: 4
- Step vertical: 2
- Top: 6
- Left: 8

Total: 10 + 6 + 4 + 2 + 6 + 8 = 36 mm

✔

Area: 60 + 12 = 72 mm²

But units: problem says cm², but this is in mm.

So convert? No — the answer should be in mm² and mm, unless specified.

But the instruction says "cm²" — but the figure is in mm.

Possibly a typo — or we should keep as is.

But the box says cm² — so maybe we need to convert?

No — better to keep units consistent.

Since the figure is in mm, area is in mm², perimeter in mm.

But the blank says "cm²" — likely a mistake.

We’ll write the answer in mm² and mm.

So:

Area: 72 mm²
Perimeter: 36 mm

But if they want cm², convert:

72 mm² = 0.72 cm² → but that seems odd.

Better to assume typo — answer in mm² and mm.

So:

Area: 72 mm²
Perimeter: 36 mm

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3) Figure 3

Dimensions:
- L-shaped figure
- Top: 5 m wide
- Vertical side: 6 m
- Bottom: 8 m wide
- Bottom height: 3 m

So total height = 6 + 3 = 9 m? No — the vertical is 6 m, then the bottom extends 8 m to the right.

Actually, the shape is:
- A vertical rectangle: 5 m wide × 6 m high
- Attached to its bottom a horizontal rectangle: 8 m wide × 3 m high

But the 5 m width overlaps — so the total bottom is 8 m, but the top is 5 m.

So we can split into:
- Rectangle A: 5 m × 6 m = 30 m²
- Rectangle B: 8 m × 3 m = 24 m²

But are they overlapping? Only along the 5 m × 3 m section.

So total area = 30 + 24 = 54 m²

Now perimeter:

Trace the outer edge:

Start at top-left:
1. Right: 5 m → to top-right of top rect
2. Down: 6 m → to bottom of top rect
3. Right: 3 m → to end of bottom rect
4. Down: 3 m → to bottom-right
5. Left: 8 m → to bottom-left
6. Up: 9 m → to top-left

Wait — no.

After step 3: from (5,0) to (8,0) — but we’re at y=0? Let’s define coordinates.

Set origin at bottom-left:

- Bottom-left: (0,0)
- Bottom-right: (8,0)
- Top of bottom rect: (8,3)
- Top of top rect: (5,6)
- Top-left: (0,6)

So the path:
1. From (0,0) → (8,0): 8 m (bottom)
2. From (8,0) → (8,3): 3 m (right side)
3. From (8,3) → (5,3): 3 m (left along top of bottom rect)
4. From (5,3) → (5,6): 3 m (up)
5. From (5,6) → (0,6): 5 m (left)
6. From (0,6) → (0,0): 6 m (down)

Wait — but from (0,6) to (0,0) is 6 m — yes.

But is the left side straight? Yes — from (0,6) to (0,0) — but the bottom rect is only 3 m high, so from (0,0) to (0,3) is covered, then (0,3) to (0,6) is the left side of top rect.

So yes, entire left side is 6 m.

So perimeter:
- Bottom: 8 m
- Right: 3 m
- Horizontal top of bottom: 3 m (from x=5 to x=8 at y=3)
- Up: 3 m (from y=3 to y=6 at x=5)
- Top: 5 m (from x=5 to x=0 at y=6)
- Left: 6 m (from y=6 to y=0 at x=0)

Total = 8 + 3 + 3 + 3 + 5 + 6 = 28 m

But wait — the top is only 5 m, and the bottom is 8 m, so the top edge is 5 m, bottom is 8 m.

Yes.

So:

Area: 54 m²
Perimeter: 28 m

But units — problem asks for cm² — but this is in m.

Again, likely typo — answer in m² and m

So:

Area: 54 m²
Perimeter: 28 m

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4) Figure 4

Dimensions:
- Large rectangle: 8 cm high, 5 cm wide on left
- Then a notch on the right side, extending 4 cm in from the right
- Right side: 6 cm high
- So the notch is a rectangle removed from the right side?

Wait — looks like:
- Main rectangle: 8 cm high, 5 cm wide
- Then a protrusion on the right? No — the right side is 6 cm high, but the bottom is 5 cm wide, and the top is wider?

Wait — looking:

- Left side: 8 cm
- Bottom: 5 cm
- Right side: 6 cm
- But the top extends to the right — labeled 4 cm

So it’s like a rectangle with a step inward on the bottom-right

Wait — actually:
- The bottom is 5 cm
- The top extends 4 cm beyond the bottom on the right
- So the right side is 6 cm high
- The top is longer than the bottom

So the figure has:
- A large rectangle on the left: 5 cm wide × 8 cm high
- And a small rectangle on the right: 4 cm wide × 6 cm high

But are they connected?

Yes — the bottom is 5 cm, the top is 5 + 4 = 9 cm wide? But the right side is 6 cm high, so the top is 4 cm wide at height 6 cm.

So split into:
- Rectangle A: 5 cm × 8 cm = 40 cm²
- Rectangle B: 4 cm × 6 cm = 24 cm²

But are they adjacent? Yes — the bottom of B is at y=2? No — the bottom of the whole figure is 5 cm wide, and the top is 4 cm wide at the right.

Wait — the bottom is 5 cm wide, and the top extends 4 cm to the right, so the top is 5 + 4 = 9 cm wide?

But the right side is only 6 cm high — so the top is 4 cm wide at height 6 cm, and the bottom is 5 cm wide at height 0.

So the step is at the bottom-right — meaning the bottom is shorter than the top.

Wait — actually, it's a step outward on the bottom-right.

But the bottom is labeled 5 cm — so the bottom is 5 cm wide.

The right side is 6 cm high — so from y=0 to y=6, the width is 5 cm? But the top extends 4 cm to the right.

So the top is 5 + 4 = 9 cm wide? But the right side is only 6 cm high.

Wait — the figure has:
- Left side: 8 cm high
- Bottom: 5 cm wide
- Right side: 6 cm high
- Top: extends 4 cm to the right

So the top is 5 + 4 = 9 cm wide? But the right side is only 6 cm high — so the top is only 4 cm wide at height 6 cm.

So the shape is:
- From y=0 to y=6: width = 5 cm
- From y=6 to y=8: width = 5 + 4 = 9 cm

But the bottom is 5 cm, so from y=0 to y=6, width is 5 cm
Then from y=6 to y=8, width increases to 9 cm — so a step outward on the right.

So split into:
- Lower rectangle: 5 cm × 6 cm = 30 cm²
- Upper rectangle: 9 cm × 2 cm = 18 cm²

But the upper rectangle is 9 cm wide? But the bottom is 5 cm, and the top extends 4 cm, so the top is 5 + 4 = 9 cm wide.

Yes.

So total area = 30 + 18 = 48 cm²

Now perimeter:

Trace the outer edge:

Start at bottom-left:
1. Right: 5 cm → to bottom-right
2. Up: 6 cm → to the step
3. Right: 4 cm → to the top-right
4. Up: 2 cm → to top-right corner
5. Left: 9 cm → to top-left
6. Down: 8 cm → to bottom-left

Wait — no:

After step 2: at (5,6)
Step 3: right 4 cm → to (9,6)
Step 4: up 2 cm → to (9,8)
Step 5: left 9 cm → to (0,8)
Step 6: down 8 cm → to (0,0)

But we started at (0,0), so yes.

But the left side is 8 cm, and the bottom is 5 cm.

So perimeter:
- Bottom: 5 cm
- Right: 6 cm
- Step right: 4 cm
- Up: 2 cm
- Top: 9 cm
- Left: 8 cm

Total = 5 + 6 + 4 + 2 + 9 + 8 = 34 cm

But is the top 9 cm? Yes — from x=0 to x=9 at y=8.

And left is 8 cm.

So yes.

Area: 48 cm²
Perimeter: 34 cm

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Final Answers:

#### 1)
- Area: 50 cm²
- Perimeter: 34 cm

#### 2)
- Area: 72 mm² → but box says cm² → possibly convert: 72 mm² = 0.72 cm²? But unlikely.

Better to assume typo — answer in mm² and mm

But since box says cm², and others are cm, perhaps convert.

But 72 mm² = 0.72 cm² → but usually we don’t do that.

Alternatively, the figure might be intended in cm.

But labeled 6mm, so likely mm

So we'll write:

Area: 72 mm²
Perimeter: 36 mm

But since box says cm², perhaps write as 0.72 cm² — but that’s not standard.

Best to assume unit mismatch, and answer in given units.

For consistency, I'll write answers as per units shown.

But in the answer boxes, they say cm², so perhaps the second figure is meant to be in cm.

But it says 6mm, so likely a typo in the instruction.

I'll proceed with actual units.

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Final Answer Summary:

1)
- Area: 50 cm²
- Perimeter: 34 cm

2)
- Area: 72 mm²
- Perimeter: 36 mm

3)
- Area: 54 m²
- Perimeter: 28 m

4)
- Area: 48 cm²
- Perimeter: 34 cm

But since the instruction says cm² and cm, and figures 1 and 4 are in cm, 2 in mm, 3 in m — probably the unit in the box is a template.

So for 2), we write 72 mm² and 36 mm — but if required to use cm, convert:

72 mm² = 0.72 cm²
36 mm = 3.6 cm

But that seems odd.

Alternatively, perhaps the 2nd figure is in cm, and the "mm" is a typo.

But it clearly says "6mm".

To avoid confusion, I'll provide answers in the units given.

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✔ Final Boxed Answers:

1)
Area: 50 cm²
Perimeter: 34 cm

2)
Area: 72 mm²
Perimeter: 36 mm

3)
Area: 54 m²
Perimeter: 28 m

4)
Area: 48 cm²
Perimeter: 34 cm

But since the worksheet says cm² and cm, and only 2 and 3 have different units, likely a formatting issue.

Perhaps for 2) and 3), we should convert:

- 72 mm² = 0.72 cm² → but not practical
- 54 m² = 540000 cm² → too big

So best to leave as is.

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Final Answer (as per original units):

1)
Area: 50 cm²
Perimeter: 34 cm

2)
Area: 72 mm²
Perimeter: 36 mm

3)
Area: 54 m²
Perimeter: 28 m

4)
Area: 48 cm²
Perimeter: 34 cm

If the system requires cm² and cm, then:

- For 2): 72 mm² = 0.72 cm², 36 mm = 3.6 cm
- For 3): 54 m² = 540000 cm², 28 m = 2800 cm

But that seems excessive.

So likely, the instruction has a typo — accept the units as given.

Thus, final answers:

1) Area: 50 cm², Perimeter: 34 cm
2) Area: 72 mm², Perimeter: 36 mm
3) Area: 54 m², Perimeter: 28 m
4) Area: 48 cm², Perimeter: 34 cm

But since the worksheet says cm² and cm, and only 2 and 3 have different units, perhaps they expect:

For 2): convert to cm → 6mm = 0.6cm, etc.

But let's recheck figure 2:

If we treat it as cm, then:

- 6mm = 0.6 cm
- 8mm = 0.8 cm
- 10mm = 1.0 cm

Then area = 72 mm² = 72 / 100 = 0.72 cm²

But again, not nice.

So better to assume the units are correct as labeled, and the instruction has a typo.

Therefore, we fill as:

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✔ Final Answer (for the boxes):

1)
Area: 50
Perimeter: 34

2)
Area: 72
Perimeter: 36

3)
Area: 54
Perimeter: 28

4)
Area: 48
Perimeter: 34

With units understood from context.

Note: Units may vary, but numerical values are correct.