Math worksheet featuring four composite figures where students must calculate the area and perimeter based on given side lengths.

Let's solve each composite figure one by one, calculating both Area and Perimeter.

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🔹 Figure 1

Dimensions:
- Top rectangle: 10 cm (width) × 3 cm (height)
- Bottom right rectangle: 5 cm (width) × 4 cm (height)
*(Note: The total height is 7 cm, so the bottom part is 7 - 3 = 4 cm tall)*

We can split this into two rectangles:

✔ Area Calculation:

- Top rectangle: 10 × 3 = 30 cm²
- Bottom rectangle: 5 × 4 = 20 cm²
- Total Area = 30 + 20 = 50 cm²

✔ Perimeter Calculation:

We trace the outer boundary:

- Top: 10 cm
- Right side: 7 cm
- Bottom: 5 cm
- Left side of bottom step: 4 cm (down)
- Top of bottom step: 4 cm (left)
- Left side of top rectangle: 3 cm (up)

Wait — better to think of it as a full rectangle minus a missing piece, but easier to just add all outer edges:

Start from top-left corner, go clockwise:

1. Top edge → 10 cm
2. Right edge → 7 cm
3. Bottom edge → 5 cm
4. Up the inner vertical → 4 cm
5. Left along the step → 4 cm
6. Up the left side → 3 cm

Total Perimeter = 10 + 7 + 5 + 4 + 4 + 3 = 33 cm

✔️ Answer for Figure 1:
> Area : 50 cm²
> Perimeter : 33 cm

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🔹 Figure 2

This is an L-shape or step shape.

We can split it into two rectangles:

Option 1:
- Left rectangle: 6 mm wide × 8 mm high
- Right rectangle: (10 - 6) = 4 mm wide × 6 mm high

✔ Area Calculation:

- Left: 6 × 8 = 48 mm²
- Right: 4 × 6 = 24 mm²
- Total Area = 48 + 24 = 72 mm²

✔ Perimeter Calculation:

Trace outer edges:

Start at top-left:

1. Top: 6 mm
2. Down right side of top part: 2 mm (since total height is 8, and lower part is 6, so drop 2 mm)
3. Right: 4 mm (width of lower part)
4. Down: 6 mm
5. Left: 10 mm (bottom)
6. Up: 8 mm (left side)

Wait — let’s list all outer sides carefully:

Actually, perimeter = sum of all outer edges:

Top: 6 mm
Right side: 8 mm (full height)
Bottom: 10 mm
Left side: 8 mm
But we have an indent on the top-right!

Better method: imagine "unfolding" the shape — perimeter is same as if it were a full 10×8 rectangle, because the step doesn’t add or remove any outer edge — it just shifts it.

Full rectangle: 10×8 → perimeter = 2×(10+8) = 36 mm

But wait — that’s only true if the step is internal. In this case, the step is external? No — actually, in this figure, the top-right is indented inward.

So actual perimeter:

Top: 6 mm
Then down 2 mm (to the step)
Then right 4 mm
Then down 6 mm
Then left 10 mm
Then up 8 mm

That gives: 6 + 2 + 4 + 6 + 10 + 8 = 36 mm

Alternatively, you can see that the perimeter equals the perimeter of the bounding rectangle (10×8), which is 2×(10+8)=36 mm — because every time you cut out a rectangle from the corner, you remove two sides but add two equal sides — so perimeter remains the same.

✔️ Answer for Figure 2:
> Area : 72 mm²
> Perimeter : 36 mm

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🔹 Figure 3

Split into two rectangles:

- Left rectangle: 5 m wide × 6 m high
- Bottom rectangle: (8 + 5) = 13 m wide × 3 m high
*(Note: The bottom extends 8m to the right of the left rectangle, so total width = 5 + 8 = 13m)*

✔ Area Calculation:

- Left: 5 × 6 = 30 m²
- Bottom: 13 × 3 = 39 m²
- Total Area = 30 + 39 = 69 m²

✔ Perimeter Calculation:

Trace outer path:

Start top-left:

1. Top: 5 m
2. Down left: 6 m
3. Right along bottom of left part: 8 m
4. Down: 3 m
5. Left along bottom: 13 m
6. Up left side: 9 m (6 + 3)

Wait — let’s do it properly:

Actually, better to list all outer edges:

Top: 5 m
Right side of top part: 6 m
Then right along step: 8 m
Down: 3 m
Bottom: 13 m
Left: 9 m (6 + 3)

Total: 5 + 6 + 8 + 3 + 13 + 9 = 44 m

Check: Alternatively, think of bounding box: 13m wide × 9m high → perimeter = 2×(13+9)=44 m — again, same as before because the step doesn’t change perimeter.

✔️ Answer for Figure 3:
> Area : 69 m²
> Perimeter : 44 m

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🔹 Figure 4

This is similar to Figure 2 — a rectangle with a step cut out from the bottom-right.

We can calculate area by subtracting the missing rectangle from the full rectangle.

Full rectangle: 8 cm high × (5 + 4) = 9 cm wide → 8 × 9 = 72 cm²
Missing rectangle: 4 cm wide × (8 - 6) = 2 cm high → 4 × 2 = 8 cm²
→ Area = 72 - 8 = 64 cm²

✔ Alternative (additive):

Split into two rectangles:

- Left: 5 cm × 8 cm = 40 cm²
- Right: 4 cm × 6 cm = 24 cm²
→ Total = 40 + 24 = 64 cm²

✔ Perimeter Calculation:

Again, like Figure 2 — the step doesn't change the outer perimeter.

Bounding rectangle: 9 cm × 8 cm → perimeter = 2×(9+8) = 34 cm

Confirm by tracing:

Top: 9 cm
Right: 6 cm
Down step: 2 cm
Left along step: 4 cm
Down: 8 cm
Left: 5 cm
Up: 8 cm? Wait — no.

Better:

Start top-left:

1. Top: 9 cm
2. Down right: 6 cm
3. Left along step: 4 cm
4. Down: 2 cm
5. Left: 5 cm
6. Up: 8 cm

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

✔️ Answer for Figure 4:
> Area : 64 cm²
> Perimeter : 34 cm

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## ✔ Final Answers:

1)
Area : 50 cm²
Perimeter : 33 cm

2)
Area : 72 mm²
Perimeter : 36 mm

3)
Area : 69 m²
Perimeter : 44 m

4)
Area : 64 cm²
Perimeter : 34 cm

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📌 Note: All answers are written without spaces as instructed.