Year 5 Perimeter of Composite Shapes Worksheets - Twinkl - Free Printable

To find the perimeter of a composite rectilinear shape, we need to add up the lengths of all the outer sides.

Key Rule: The perimeter is the total distance around the outside of the shape.

Let's look at the shapes on the right side of the sheet (Section C), as these have numbers provided to solve. I will calculate the perimeter for each labeled shape (a through h).

Shape a:
- Top side: 8 cm
- Right side (top part): 4 cm
- Middle horizontal step: 6 cm
- Middle vertical step: 3 cm
- Bottom right horizontal: 5 cm
- Bottom vertical: 7 cm
- Bottom horizontal: 19 cm
- Left vertical: This side is missing a label, but in rectilinear shapes, opposite vertical sides usually sum up to the same total height if they are parallel. Let's trace the full loop.
Actually, a simpler way for these "staircase" or indented shapes is to look at the bounding box or just sum every visible segment. Let's list every segment shown on the outline:
1. Top: 8 cm
2. Right-down: 4 cm
3. Left-in: 6 cm
4. Down: 3 cm
5. Right-out: 5 cm
6. Down: 7 cm
7. Bottom-left: 19 cm
8. Up (Left side): We need this length. Looking at the vertical segments on the right: 4 + 3 + 7 = 14 cm. So the left side must be 14 cm.
*Wait, let's re-examine shape 'a'.*
The labels are: Top=8, Right-top=4, Inner-horizontal=6, Inner-vertical=3, Lower-right-horizontal=5, Lower-vertical=7, Bottom=19.
Let's check the horizontal widths: Top (8) + Inner (6) + Lower-right (5) = 19. This matches the bottom width of 19. Good.
Let's check the vertical heights: Right-top (4) + Inner-vertical (3) + Lower-vertical (7) = 14. So the far-left vertical side is 14 cm.

Perimeter = Sum of all outer edges:
$8 + 4 + 6 + 3 + 5 + 7 + 19 + 14$
Calculation:
$8 + 4 = 12$
$12 + 6 = 18$
$18 + 3 = 21$
$21 + 5 = 26$
$26 + 7 = 33$
$33 + 19 = 52$
$52 + 14 = 66$

Perimeter of a = 66 cm

Shape b:
- Top: 10 cm
- Right-top: 4 cm
- Inner-horizontal: 6 cm
- Inner-vertical: 3 cm
- Lower-right-horizontal: 4 cm
- Lower-vertical: 5 cm
- Bottom: 20 cm
- Left-vertical: Sum of right-side verticals = $4 + 3 + 5 = 12$ cm.
Check horizontals: $10 + 6 + 4 = 20$. Matches bottom.

Perimeter = $10 + 4 + 6 + 3 + 4 + 5 + 20 + 12$
Calculation:
$10 + 4 = 14$
$14 + 6 = 20$
$20 + 3 = 23$
$23 + 4 = 27$
$27 + 5 = 32$
$32 + 20 = 52$
$52 + 12 = 64$

Perimeter of b = 64 cm

Shape c:
- Top: 11 cm
- Right-top: 5 cm
- Inner-horizontal: 7 cm
- Inner-vertical: 4 cm
- Lower-right-horizontal: 6 cm
- Lower-vertical: 9 cm
- Bottom: 24 cm
- Left-vertical: Sum of right-side verticals = $5 + 4 + 9 = 18$ cm.
Check horizontals: $11 + 7 + 6 = 24$. Matches bottom.

Perimeter = $11 + 5 + 7 + 4 + 6 + 9 + 24 + 18$
Calculation:
$11 + 5 = 16$
$16 + 7 = 23$
$23 + 4 = 27$
$27 + 6 = 33$
$33 + 9 = 42$
$42 + 24 = 66$
$66 + 18 = 84$

Perimeter of c = 84 cm

Shape d:
- Top: 8 cm
- Right-top: 5 cm
- Inner-horizontal: 11 cm
- Inner-vertical: 7 cm
- Lower-right-horizontal: 7 cm
- Lower-vertical: 10 cm
- Bottom: 26 cm
- Left-vertical: Sum of right-side verticals = $5 + 7 + 10 = 22$ cm.
Check horizontals: $8 + 11 + 7 = 26$. Matches bottom.

Perimeter = $8 + 5 + 11 + 7 + 7 + 10 + 26 + 22$
Calculation:
$8 + 5 = 13$
$13 + 11 = 24$
$24 + 7 = 31$
$31 + 7 = 38$
$38 + 10 = 48$
$48 + 26 = 74$
$74 + 22 = 96$

Perimeter of d = 96 cm

Shape e:
This shape is different. It looks like a large rectangle with a rectangular chunk taken out of the top right, or an L-shape rotated.
Labels:
- Left vertical: 12 cm
- Bottom horizontal: 18 cm
- Right vertical (bottom part): 8 cm
- Top horizontal (left part): 10 cm
- Inner vertical (going down): ?
- Inner horizontal (going right): ?
Wait, looking closely at 'e':
It has:
- Left side: 12 cm
- Bottom side: 18 cm
- Right side (lower): 8 cm
- Top side (left): 10 cm
There is an inner corner.
Let's deduce the missing sides.
Total Width = 18 cm. Top-left part is 10 cm. So the inner horizontal part (the rest of the width) is $18 - 10 = 8$ cm? No, that's not how the lines are drawn.
Let's trace the perimeter clockwise starting from top-left corner:
1. Top edge: 10 cm
2. Inner vertical edge going DOWN: Let's call this $x$.
3. Inner horizontal edge going RIGHT: Let's call this $y$.
4. Right edge going UP? No, the label 8cm is on the rightmost vertical edge.
Let's re-read the shape structure.
It looks like an L-shape lying on its back? Or a standard L?
Left side is 12. Bottom is 18.
Top side is 10.
Right side is 8.
This implies there is a "step".
If the total height is 12 (left side) and the right side is 8, then the inner vertical drop is $12 - 8 = 4$ cm.
If the total width is 18 (bottom) and the top side is 10, then the inner horizontal run is $18 - 10 = 8$ cm.
So the sides are:
- Left: 12
- Top: 10
- Inner Vertical: 4 (calculated as $12-8$)
- Inner Horizontal: 8 (calculated as $18-10$)
- Right: 8
- Bottom: 18

Perimeter = $12 + 10 + 4 + 8 + 8 + 18$
Calculation:
$12 + 10 = 22$
$22 + 4 = 26$
$26 + 8 = 34$
$34 + 8 = 42$
$42 + 18 = 60$

Perimeter of e = 60 cm

Shape f:
Similar L-shape logic.
- Left vertical: 15 cm
- Bottom horizontal: 20 cm
- Right vertical: 10 cm
- Top horizontal: 12 cm
Missing inner sides:
- Inner vertical drop: Total Height (15) - Right Side (10) = 5 cm.
- Inner horizontal run: Total Width (20) - Top Side (12) = 8 cm.

Sides to add:
1. Left: 15
2. Top: 12
3. Inner Vertical: 5
4. Inner Horizontal: 8
5. Right: 10
6. Bottom: 20

Perimeter = $15 + 12 + 5 + 8 + 10 + 20$
Calculation:
$15 + 12 = 27$
$27 + 5 = 32$
$32 + 8 = 40$
$40 + 10 = 50$
$50 + 20 = 70$

Perimeter of f = 70 cm

Shape g:
- Left vertical: 16 cm
- Bottom horizontal: 25 cm
- Right vertical: 12 cm
- Top horizontal: 14 cm
Missing inner sides:
- Inner vertical drop: $16 - 12 = 4$ cm.
- Inner horizontal run: $25 - 14 = 11$ cm.

Sides to add:
1. Left: 16
2. Top: 14
3. Inner Vertical: 4
4. Inner Horizontal: 11
5. Right: 12
6. Bottom: 25

Perimeter = $16 + 14 + 4 + 11 + 12 + 25$
Calculation:
$16 + 14 = 30$
$30 + 4 = 34$
$34 + 11 = 45$
$45 + 12 = 57$
$57 + 25 = 82$

Perimeter of g = 82 cm

Shape h:
- Left vertical: 20 cm
- Bottom horizontal: 30 cm
- Right vertical: 15 cm
- Top horizontal: 18 cm
Missing inner sides:
- Inner vertical drop: $20 - 15 = 5$ cm.
- Inner horizontal run: $30 - 18 = 12$ cm.

Sides to add:
1. Left: 20
2. Top: 18
3. Inner Vertical: 5
4. Inner Horizontal: 12
5. Right: 15
6. Bottom: 30

Perimeter = $20 + 18 + 5 + 12 + 15 + 30$
Calculation:
$20 + 18 = 38$
$38 + 5 = 43$
$43 + 12 = 55$
$55 + 15 = 70$
$70 + 30 = 100$

Perimeter of h = 100 cm

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Final Answer:
Here are the calculated perimeters for the shapes in Section C:

* Shape a: 66 cm
* Shape b: 64 cm
* Shape c: 84 cm
* Shape d: 96 cm
* Shape e: 60 cm
* Shape f: 70 cm
* Shape g: 82 cm
* Shape h: 100 cm