Area and perimeter of compound shapes|KS2 Maths|Geometry|Teachit - Free Printable

Of course! Let's solve each compound shape one by one, calculating both the area and the perimeter. We’ll break each shape into simpler rectangles (or subtract areas) to make it easier.

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## 🔷 SHAPE 1 (Top Left - Purple L-shape)

Dimensions:

- Overall width: 6 cm
- Overall height: 5 cm
- Top left rectangle: 3 cm wide × 3 cm high
- Bottom right rectangle: 3 cm wide × 2 cm high

We can split this into two rectangles:

#### ➤ Area:
- Rectangle A (top left): 3 cm × 3 cm = 9 cm²
- Rectangle B (bottom part): 6 cm × 2 cm = 12 cm²
*(Note: The bottom part spans full 6 cm width, height 2 cm)*

✔ Total Area = 9 + 12 = 21 cm²

#### ➤ Perimeter:
Trace the outer edges:
- Top: 3 cm (left part) + 3 cm (right part) = 6 cm
- Right side: 2 cm (bottom) + 3 cm (vertical step) = 5 cm
- Bottom: 6 cm
- Left side: 5 cm

Wait — let’s list all sides carefully:

Start at top-left corner, go clockwise:
- Right → 3 cm
- Down → 3 cm
- Right → 3 cm
- Down → 2 cm
- Left → 6 cm
- Up → 5 cm

Add them up:
3 + 3 + 3 + 2 + 6 + 5 = 22 cm

✔ Perimeter = 22 cm

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## 🔷 SHAPE 2 (Top Right - Pink Shape)

This looks like a large rectangle with a small rectangle cut out from the bottom right.

Dimensions:

- Large rectangle: 7 cm wide × 8 cm high → area = 56 cm²
- Cut-out rectangle: 1 cm × 1 cm → area = 1 cm²

#### ➤ Area:
56 – 1 = 55 cm²

#### ➤ Perimeter:
Even though we cut out a piece, the perimeter *increases* because we now have 2 extra inner edges.

Original perimeter of big rectangle:
2 × (7 + 8) = 2 × 15 = 30 cm

Cutting out a 1×1 square from the corner adds 2 new sides (each 1 cm) — because you remove 1 cm from the bottom and 1 cm from the right side, but add 1 cm on the top of the cut and 1 cm on the left of the cut.

So: 30 + 1 + 1 = 32 cm

✔ Area = 55 cm², Perimeter = 32 cm

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## 🔷 SHAPE 3 (Middle Left - Green L-shape)

Split into two rectangles:

- Left vertical rectangle: 4 m wide × 5 m high = 20 m²
- Bottom horizontal rectangle: 5 m long × 1 m high = 5 m²

But wait — the horizontal part starts after 4 m, so total width is 9 m. So the horizontal part is (9 – 4) = 5 m long, yes.

✔ Area = 20 + 5 = 25 m²

#### ➤ Perimeter:

Trace outer edges:
- Top: 4 m
- Right side down: 4 m (from top of vertical part)
- Then right: 5 m (horizontal part)
- Down: 1 m
- Left: 9 m (bottom)
- Up: 5 m (left side)

Wait — better to list all sides clockwise:

Start at top-left:
- Right → 4 m
- Down → 5 m
- Right → 5 m
- Down → 1 m
- Left → 9 m
- Up → 5 m? No — that would be wrong.

Actually, the left side is 5 m, then bottom is 9 m, then up the right side: 1 m (from horizontal part) + 4 m (from vertical part) = 5 m.

Let’s do it step-by-step:

- Top edge: 4 m
- Right edge (down): 5 m
- Bottom edge (right to left): 9 m
- Left edge (up): 5 m

Wait — that gives 4 + 5 + 9 + 5 = 23 m — but we missed the “step” inside!

Actually, when you go down the right side, after 4 m down, you turn right for 5 m, then down 1 m, then left 9 m, then up 5 m.

So sides are:
- Top: 4 m
- Down: 4 m
- Right: 5 m
- Down: 1 m
- Left: 9 m
- Up: 5 m

Total: 4 + 4 + 5 + 1 + 9 + 5 = 28 m

✔ Area = 25 m², Perimeter = 28 m

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## 🔷 SHAPE 4 (Middle Right - Blue Shape)

Looks like a big rectangle with a small rectangle cut out from the bottom left.

Big rectangle: 10 m wide × 6 m high → area = 60 m²
Cut-out: 2 m × 2 m → area = 4 m²

#### ➤ Area:
60 – 4 = 56 m²

#### ➤ Perimeter:

Original big rectangle perimeter: 2 × (10 + 6) = 32 m

Cutting out a 2×2 square from the corner adds 2 new inner edges (each 2 m), so total perimeter = 32 + 2 + 2 = 36 m

✔ Area = 56 m², Perimeter = 36 m

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## 🔷 SHAPE 5 (Bottom - Orange Shape)

This is a large rectangle with a rectangular “notch” cut out from the center of the bottom.

Big rectangle: 12 m × 8 m → area = 96 m²
Notch: 5 m wide × 4 m high → area = 20 m²

#### ➤ Area:
96 – 20 = 76 m²

#### ➤ Perimeter:

Original perimeter: 2 × (12 + 8) = 40 m

Now, cutting out the notch adds 2 vertical sides (each 4 m) and removes 5 m from the bottom — BUT we also add the top of the notch (5 m).

So net change: we remove 5 m from bottom, add 5 m (top of notch) + 4 m (left side) + 4 m (right side) = +8 m

Thus, perimeter = 40 + 8 = 48 m

✔ Area = 76 m², Perimeter = 48 m

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## ✔ FINAL ANSWERS:

| Shape | Area | Perimeter |
|-------|--------------|---------------|
| 1 | 21 cm² | 22 cm |
| 2 | 55 cm² | 32 cm |
| 3 | 25 m² | 28 m |
| 4 | 56 m² | 36 m |
| 5 | 76 m² | 48 m |

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Let me know if you’d like a diagram or visual breakdown for any shape!