Perimeter of Different Shapes Worksheet - Free Printable

Let’s solve each shape one by one. Remember: perimeter is the total distance around the outside of a shape. We add up all the side lengths — even the missing ones we have to figure out first!

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Shape 1)
We’re given:
- Left side = 11 cm
- Bottom = 15 cm
- Right side = 9 cm
- Top right horizontal = 9 cm

We need to find the missing top left horizontal and the small vertical on the right (but wait — actually, looking at the shape, it’s like a rectangle with a bite taken out of the top right).

Actually, let’s think differently. In rectilinear shapes (all angles are right angles), opposite sides often match up when you “complete” the rectangle.

Total width (bottom) = 15 cm
Top has two parts: unknown left part + 9 cm → so unknown left part = 15 - 9 = 6 cm

Total height (left side) = 11 cm
Right side has two parts: 9 cm (given) + unknown top part → so unknown top part = 11 - 9 = 2 cm

Now list ALL sides going around:

Start from bottom left, go clockwise:
- Bottom: 15 cm
- Right lower: 9 cm
- Right upper (small vertical): 2 cm ← we just found this
- Top right horizontal: 9 cm
- Top left horizontal: 6 cm ← we just found this
- Left side: 11 cm

Add them:
15 + 9 + 2 + 9 + 6 + 11 = Let’s compute step by step:

15 + 9 = 24
24 + 2 = 26
26 + 9 = 35
35 + 6 = 41
41 + 11 = 52 cm

✔ Perimeter for Shape 1 = 52 cm

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Shape 2)
Given:
- Left side = 22 mm
- Bottom = 18 mm
- Top = 25 mm
- Right upper vertical = 6 mm

This shape looks like a rectangle with a notch cut out of the bottom right.

Total width (top) = 25 mm
Bottom has two parts: 18 mm + unknown right part → unknown = 25 - 18 = 7 mm

Total height (left) = 22 mm
Right side has two parts: 6 mm (top) + unknown bottom part → unknown = 22 - 6 = 16 mm

Now walk around the shape clockwise starting from bottom left:

- Bottom left horizontal: 18 mm
- Bottom right vertical (up into the notch): 16 mm ← we found this
- Notch horizontal (rightward): 7 mm ← we found this
- Notch vertical (up): 6 mm (given)
- Top horizontal: 25 mm
- Left vertical: 22 mm

Wait — that doesn’t seem right. Actually, if we go around the outer edge:

Better path: Start at bottom left corner, go right along bottom (18 mm), then UP the inner vertical (which is 16 mm? Wait no — let’s redraw mentally.

Actually, standard way: in such L-shapes or notched rectangles, the perimeter equals the perimeter of the full rectangle PLUS twice the depth of the notch — but maybe easier to just trace all outer edges.

Let me label all sides clearly:

Imagine the full rectangle would be 25 mm wide and 22 mm tall.

But there’s a rectangular notch removed from the bottom right. The notch has:
- Width = 25 - 18 = 7 mm
- Height = 22 - 6 = 16 mm? Wait, no — the right side shows 6 mm at the top, meaning the remaining vertical below it is 22 - 6 = 16 mm, which is the height of the notch.

When you remove a rectangle from the corner, you lose two sides but gain two new sides of the same length — so perimeter stays the same as the original rectangle! Is that true?

Original rectangle: 25 mm × 22 mm → perimeter = 2×(25+22) = 2×47 = 94 mm

But let’s verify by adding actual outer sides:

Going clockwise from bottom left:

1. Bottom: 18 mm
2. Up the inner vertical: this is the height of the notch = 22 - 6 = 16 mm
3. Right along the notch top: 7 mm (since 25 - 18 = 7)
4. Up the rightmost vertical: 6 mm
5. Left along top: 25 mm
6. Down left side: 22 mm

Wait — that adds extra. Actually, after step 4 (up 6 mm), we’re at the top right corner, then we go left 25 mm to top left, then down 22 mm to start. But we already went up 16 mm and then 6 mm — that’s 22 mm total on the right, which matches.

But now let’s add the path:

Path:
Start at bottom left → right 18 mm → up 16 mm → right 7 mm → up 6 mm → left 25 mm → down 22 mm → back to start.

Wait, that’s 6 segments, but we should only have 6 sides for this shape? Actually, yes.

Add them:

18 + 16 + 7 + 6 + 25 + 22

Calculate:

18 + 16 = 34
34 + 7 = 41
41 + 6 = 47
47 + 25 = 72
72 + 22 = 94 mm

Yes! Same as full rectangle. So perimeter = 94 mm

✔ Perimeter for Shape 2 = 94 mm

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Shape 3)
Given:
- Top = 2.5 m
- Left upper vertical = 0.5 m
- Left lower horizontal = 0.5 m
- Bottom = 1 m
- Right lower vertical = 0.8 m
- Right upper vertical = 1.2 m

This is a T-shaped or inverted U? Actually, looks like a rectangle with a protrusion downward in the middle.

Let’s find missing sides.

First, total width = top = 2.5 m
Bottom has three parts? No — bottom is labeled 1 m, but there are two side bottoms.

Actually, looking at the shape: it’s symmetric? Not necessarily.

Left side: from top, down 0.5 m, then right 0.5 m, then down some amount, then right 1 m, then up 0.8 m, then right some amount, then up 1.2 m to meet top.

Wait — better to use the fact that horizontal segments must add up.

Total width = 2.5 m

On the bottom level, we have:
- Left horizontal segment: 0.5 m (given)
- Middle bottom: 1 m (given)
- Right horizontal segment: ? → must be 2.5 - 0.5 - 1 = 1.0 m

Similarly, vertically:

Left side total height: from top to bottom of left leg = 0.5 m (down) + ? (down more)

Actually, the right side has two verticals: 0.8 m (lower) and 1.2 m (upper) → total right height = 0.8 + 1.2 = 2.0 m

So the entire shape height is 2.0 m.

On the left, we have 0.5 m down, then later another down segment. Since total height is 2.0 m, and we’ve gone down 0.5 m initially, the remaining down on left must be 2.0 - 0.5 = 1.5 m? But wait, there’s a horizontal in between.

Actually, let’s trace the perimeter.

List all outer sides clockwise from top left:

1. Top: 2.5 m (right)
2. Right upper vertical: 1.2 m (down)
3. Right horizontal (inward?): wait, no — after going down 1.2 m, we go left? Actually, looking at the diagram description, after right upper vertical 1.2 m down, we go left along a horizontal? But it’s not labeled.

I think I need to infer missing sides based on alignment.

Since it’s rectilinear, horizontal lines align.

Total width = 2.5 m

The bottom consists of three horizontal segments:
- Left: 0.5 m
- Middle: 1 m
- Right: let’s call it x → 0.5 + 1 + x = 2.5 → x = 1.0 m

Vertically, the total height can be found from the right side: 0.8 m (bottom part) + 1.2 m (top part) = 2.0 m

On the left side, we have:
- From top, down 0.5 m
- Then right 0.5 m
- Then down y m (this is the left leg of the "T")
- Then right 1 m (bottom middle)
- Then up 0.8 m (right lower vertical)
- Then right 1.0 m (we calculated)
- Then up 1.2 m to close

But the down y on left must equal the total height minus the initial 0.5 m? Total height is 2.0 m, so y = 2.0 - 0.5 = 1.5 m? But then when we go up 0.8 m on the right, that doesn't match.

Actually, the vertical drop on the left after the first 0.5 m should be such that when we go across the bottom and up the right, it connects.

Perhaps better: the vertical distance from the top to the bottom of the left protrusion is 0.5 m + z, and on the right, from top to bottom of right protrusion is 1.2 m + 0.8 m = 2.0 m, but they may not be at the same level.

Wait — in rectilinear shapes, the sum of upward movements equals sum of downward movements, and same for left/right.

Let’s list all horizontal segments (left-right direction):

Top: 2.5 m (→)

Then, after going down right side 1.2 m, we go left? Actually, no — typically in such diagrams, after the right upper vertical, we go left along a horizontal that is part of the "arm".

I recall that for these problems, you can often find missing sides by subtracting known parts from totals.

For horizontal directions:

The total length moving right must equal total length moving left.

Similarly for up/down.

But perhaps simplest: draw it mentally.

Assume the shape has:

- A top bar: 2.5 m wide, height say h1
- A stem hanging down in the middle: width 1 m, height h2
- On the left, there's a small extension: from the left end of top bar, down 0.5 m, then right 0.5 m, then down to connect to the stem? This is messy.

Looking back at the given labels:

Labelled sides:
- Top: 2.5 m
- Left: 0.5 m (vertical)
- Then a horizontal: 0.5 m (to the right)
- Then a vertical down: unlabeled, let's call it A
- Then horizontal right: 1 m (bottom)
- Then vertical up: 0.8 m
- Then horizontal right: unlabeled, call it B
- Then vertical up: 1.2 m to meet top

Also, on the right, from top, down 1.2 m, then left? No, the 1.2 m is on the right side, so after top, we go down 1.2 m on the right, then left along a horizontal? But it's not labeled.

Actually, the right side has two verticals: the upper one is 1.2 m, lower one is 0.8 m, so between them there must be a horizontal segment.

Similarly on the left.

To simplify, let's calculate the missing horizontal and vertical segments using the fact that opposite sides balance.

Total width = 2.5 m

The bottom row has three horizontal segments: left 0.5 m, middle 1 m, right ? → as before, 2.5 - 0.5 - 1 = 1.0 m for the right bottom horizontal.

Now for heights:

The left side has a vertical of 0.5 m at the top, then after moving right 0.5 m, it goes down some amount, say C, to reach the bottom level.

The right side has a vertical of 1.2 m at the top, then after moving left some amount, it goes down 0.8 m to the bottom level.

The key is that the bottom level is straight, so the vertical drops on left and right must bring us to the same level.

From the top, on the left, we go down 0.5 m, then later down C m, so total down on left = 0.5 + C

On the right, we go down 1.2 m, then later down 0.8 m, so total down on right = 1.2 + 0.8 = 2.0 m

Since the shape is closed, the total down must equal total up, but for the overall height, the maximum depth should be consistent.

Actually, the point where the left stem meets the bottom should be at the same level as where the right stem meets the bottom.

So the vertical distance from top to bottom on the left path is 0.5 + C

On the right path, it's 1.2 + 0.8 = 2.0 m

Therefore, 0.5 + C = 2.0 → C = 1.5 m

Similarly, the horizontal segments: after going down 0.5 m on left, we go right 0.5 m, then down 1.5 m, then right 1 m (bottom), then up 0.8 m, then right 1.0 m (as calculated), then up 1.2 m.

Now, what about the horizontal between the right upper vertical and the right lower vertical? After going down 1.2 m on the right, we need to go left to connect to the up 0.8 m part.

The distance we go left there should be equal to the right bottom horizontal, which is 1.0 m, because the bottom is 1.0 m on the right, and the top is aligned.

Let's list all sides in order, clockwise from top left:

1. Top: 2.5 m (→)
2. Right upper vertical: 1.2 m (↓)
3. Right middle horizontal: ? (←) — this should be the same as the right bottom horizontal, which is 1.0 m, because the shape is rectilinear and the bottom right is 1.0 m wide.
So: 1.0 m (←)
4. Right lower vertical: 0.8 m (↓)
5. Bottom right horizontal: 1.0 m (←) — wait, no, if we're at the bottom right corner after step 4, and we go left, but the bottom middle is 1 m, so actually after step 4, we are at the bottom right of the right protrusion, then we go left along the bottom.

Perhaps better to start from bottom left.

Start at bottom left corner:

- Go right along bottom left horizontal: 0.5 m
- Go up the left lower vertical: this is C = 1.5 m (↑)
- Go right along the left middle horizontal: 0.5 m (→)
- Go up the left upper vertical: 0.5 m (↑) — but wait, we already went up 1.5 m, then up 0.5 m would be too much.

I think I have a confusion in direction.

Let me define the path carefully.

Assume we start at the top left corner.

Move right along top: 2.5 m → to top right corner.

Move down along right side: first 1.2 m ↓ to a point, then we move left horizontally for some distance, say D, then down 0.8 m ↓ to bottom right corner.

From bottom right corner, move left along bottom: this bottom has three parts, but the rightmost part is from bottom right to the start of the middle bottom. Since the right bottom horizontal is 1.0 m (as calculated earlier), so move left 1.0 m.

Then, from there, move up 0.8 m ↑ (this is the right lower vertical, but we already used it? No.

Perhaps the 0.8 m is the vertical on the right side of the middle stem.

Let's look for a different approach.

In many such worksheets, for shape 3, the missing sides can be found by:

- The horizontal segment on the right between the two verticals: since the top is 2.5 m, and the left has a 0.5 m horizontal after the first drop, and the bottom middle is 1 m, etc.

Notice that the total length of all horizontal segments on the top and bottom should balance.

Another way: the perimeter can be calculated by adding all given sides and the inferred ones.

Given sides for shape 3:
- 2.5 m (top)
- 0.5 m (left upper vertical)
- 0.5 m (left middle horizontal)
- 1 m (bottom middle)
- 0.8 m (right lower vertical)
- 1.2 m (right upper vertical)

Missing sides:
- Left lower vertical: let's call it V1
- Right middle horizontal: H1
- Right bottom horizontal: H2
- And possibly others.

From geometry:

The total width is 2.5 m.

The bottom consists of:
- Left bottom horizontal: this is the same as the left middle horizontal? No.

Actually, the left part: from the left end, after going down 0.5 m, we go right 0.5 m, then down V1, then right 1 m (bottom middle), then up 0.8 m, then right H2, then up 1.2 m to meet the top.

The top is 2.5 m, so the sum of the horizontal segments at the top level must be 2.5 m.

At the top level, we have the full 2.5 m.

At the bottom level, we have three segments: left, middle, right.

The left bottom horizontal is the same as the left middle horizontal? No, the left middle horizontal is at a higher level.

Perhaps the shape has:

- A top rectangle: width 2.5 m, height 1.2 m (since right upper vertical is 1.2 m)
- Below that, on the left, a rectangle extending down: width 0.5 m, height 0.5 m? But then there's more.

I recall that in such problems, the missing vertical on the left can be found as: total height on right is 1.2 + 0.8 = 2.0 m, and on left, we have 0.5 m already, so the additional down is 2.0 - 0.5 = 1.5 m.

Similarly, the horizontal on the right between the two verticals: since the bottom right horizontal is 1.0 m (because 2.5 - 0.5 - 1 = 1.0), and the top is 2.5 m, the horizontal segment at the middle right must be 1.0 m to match.

So let's assume:

Missing sides:
- Left lower vertical: 1.5 m
- Right middle horizontal: 1.0 m (leftward)
- Right bottom horizontal: 1.0 m (leftward) — but that might be double-counting.

Let's list the perimeter path:

Start at top left.

1. Right 2.5 m (top)
2. Down 1.2 m (right upper)
3. Left 1.0 m (right middle horizontal) — this is the width of the right protrusion at that level
4. Down 0.8 m (right lower vertical)
5. Left 1.0 m (bottom right horizontal) — but this would be the same as step 3? No.

After step 4, we are at the bottom right corner of the right protrusion. Then we go left along the bottom. The bottom has from right to left: first the right bottom horizontal, which is 1.0 m, then the middle bottom 1 m, then the left bottom horizontal.

But the left bottom horizontal is not directly given; however, from the left side, after going down 0.5 m and right 0.5 m, we go down 1.5 m to the bottom, so the left bottom horizontal is the segment from there to the start of the middle bottom.

Actually, the bottom is continuous: from left to right, it's 0.5 m (left) + 1 m (middle) + 1.0 m (right) = 2.5 m, good.

So from bottom right corner, go left 1.0 m (right bottom horizontal) to the start of the middle bottom.

Then go left 1 m (middle bottom) to the start of the left bottom.

Then go up the left lower vertical: 1.5 m (since total height is 2.0 m, and we've only gone down 0.5 m on left so far? Let's see.

From the bottom left corner, after going left 1 m and 1.0 m, we are at the bottom left of the left protrusion. Then we go up 1.5 m to the point where we had gone right 0.5 m earlier.

Then from there, go left 0.5 m (left middle horizontal) to the left side.

Then go up 0.5 m (left upper vertical) to the top left corner.

So the path is:

1. Top: 2.5 m →
2. Right upper vertical: 1.2 m ↓
3. Right middle horizontal: 1.0 m ←
4. Right lower vertical: 0.8 m ↓
5. Bottom right horizontal: 1.0 m ←
6. Bottom middle horizontal: 1.0 m ← (wait, given as 1 m, so 1.0 m)
7. Bottom left horizontal: 0.5 m ← (given as 0.5 m on left, but this is the bottom left segment)
8. Left lower vertical: 1.5 m ↑
9. Left middle horizontal: 0.5 m ← (given)
10. Left upper vertical: 0.5 m ↑

But this has 10 segments, and we're back to start, but let's check if it closes.

After step 10, we are at top left, good.

Now add all lengths:

1. 2.5
2. 1.2
3. 1.0
4. 0.8
5. 1.0
6. 1.0 (bottom middle)
7. 0.5 (bottom left)
8. 1.5 (left lower vertical)
9. 0.5 (left middle horizontal)
10. 0.5 (left upper vertical)

Sum: let's calculate:

2.5 + 1.2 = 3.7
3.7 + 1.0 = 4.7
4.7 + 0.8 = 5.5
5.5 + 1.0 = 6.5
6.5 + 1.0 = 7.5
7.5 + 0.5 = 8.0
8.0 + 1.5 = 9.5
9.5 + 0.5 = 10.0
10.0 + 0.5 = 10.5 m

Is that correct? Let me verify with another method.

Notice that the shape can be seen as a large rectangle minus some parts, but perhaps not.

Total horizontal movement: all right moves and left moves should cancel, but for perimeter, we add all.

Another way: the perimeter is the sum of all outer edges.

Given that, and our calculation gives 10.5 m, and it makes sense.

We can group:

Vertical sides:
- Left: 0.5 + 1.5 = 2.0 m
- Right: 1.2 + 0.8 = 2.0 m
- Plus the internal verticals? No, in perimeter, only outer.

In our path, we have vertical segments: 1.2, 0.8, 1.5, 0.5 — sum 1.2+0.8=2.0, 1.5+0.5=2.0, total vertical 4.0 m

Horizontal segments: 2.5, 1.0, 1.0, 1.0, 0.5, 0.5 — sum 2.5+1.0+1.0+1.0+0.5+0.5 = let's see: 2.5+1.0=3.5, +1.0=4.5, +1.0=5.5, +0.5=6.0, +0.5=6.5 m

Total perimeter = vertical + horizontal = 4.0 + 6.5 = 10.5 m

Yes.

So perimeter for Shape 3 = 10.5 m

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Shape 4)
Given:
- Bottom = 5 cm
- Left lower vertical = 1 cm
- Left middle horizontal = 1.5 cm
- Left upper vertical = 2.5 cm
- Top = 2.5 cm
- Right lower vertical = 2 cm

This looks like a staircase or stepped shape.

Find missing sides.

Total width = bottom = 5 cm

Top = 2.5 cm, so the overhang on the right must be 5 - 2.5 = 2.5 cm, but there's a step.

Let's trace the path.

Start at bottom left.

Go right along bottom: 5 cm → to bottom right corner.

Go up right lower vertical: 2 cm ↑

Then, since it's rectilinear, we go left along a horizontal. How far? The top is 2.5 cm, and the left has steps.

From the right, after going up 2 cm, we go left for some distance, say H1, then up some vertical, then left to meet the top.

On the left side, we have:
- From bottom, up 1 cm
- Then right 1.5 cm
- Then up 2.5 cm
- Then right to meet the top.

The top is 2.5 cm, so from the left upper corner, we go right 2.5 cm to the right upper corner.

Now, the vertical on the right: after going up 2 cm, we need to go up more to reach the top level.

Total height on left: 1 cm + 2.5 cm = 3.5 cm

On right, we have 2 cm so far, so the remaining up is 3.5 - 2 = 1.5 cm

Similarly, horizontally, after going up 2 cm on right, we go left for a distance that should match the left middle horizontal or something.

Let's list the path clockwise from bottom left:

1. Bottom: 5 cm →
2. Right lower vertical: 2 cm ↑
3. Right middle horizontal: ? ← — this should be the width of the right step. Since the top is 2.5 cm, and the bottom is 5 cm, and on the left there is a 1.5 cm horizontal, likely this is 1.5 cm or something.

Actually, the total width is 5 cm.

The top is 2.5 cm, so the difference is 2.5 cm, which is distributed on the sides.

On the left, after going up 1 cm, we go right 1.5 cm, so the left part extends 1.5 cm inward.

On the right, after going up 2 cm, we go left for some distance, say X, then up 1.5 cm (as calculated), then left to meet the top.

The distance from the right edge to the top right corner is 0, but the top starts at some point.

Perhaps the horizontal segment after the 2 cm up on right is equal to the left middle horizontal, which is 1.5 cm, by symmetry or design.

Assume that.

So:

3. Right middle horizontal: 1.5 cm ←
4. Right upper vertical: 1.5 cm ↑ (since 3.5 - 2 = 1.5)
5. Top: 2.5 cm ← (from right to left)
6. Left upper vertical: 2.5 cm ↓ — but wait, we are at top left, and we need to go down.

After step 5, we are at top left corner.

Then go down left upper vertical: 2.5 cm ↓
7. Left middle horizontal: 1.5 cm → (given)
8. Left lower vertical: 1 cm ↓
9. Then we are at bottom left, but we have the bottom already done.

From step 8, after going down 1 cm, we are at the bottom left corner, and we started there, so we need to close, but we have the bottom from left to right already in step 1.

In this path, we have:

1. 5 cm (bottom)
2. 2 cm (up right)
3. 1.5 cm (left)
4. 1.5 cm (up)
5. 2.5 cm (left) — top
6. 2.5 cm (down) — left upper vertical
7. 1.5 cm (right) — left middle horizontal
8. 1 cm (down) — left lower vertical

But after step 8, we are at the bottom left, and we have covered the bottom in step 1, so this is a closed loop, but we have 8 segments.

Add them:

5 + 2 + 1.5 + 1.5 + 2.5 + 2.5 + 1.5 + 1

Calculate step by step:

5 + 2 = 7
7 + 1.5 = 8.5
8.5 + 1.5 = 10
10 + 2.5 = 12.5
12.5 + 2.5 = 15
15 + 1.5 = 16.5
16.5 + 1 = 17.5 cm

Is this correct? Let's verify the heights and widths.

Total height: left side: 2.5 cm (upper) + 1 cm (lower) = 3.5 cm
Right side: 2 cm (lower) + 1.5 cm (upper) = 3.5 cm, good.

Total width: bottom 5 cm
Top 2.5 cm
The horizontal segments: on the bottom, 5 cm
On the top, 2.5 cm
In the middle, we have left middle horizontal 1.5 cm (going right), and right middle horizontal 1.5 cm (going left), so they are at different levels.

The perimeter should include all outer edges, and our path seems to cover it.

Another way: the shape can be seen as a rectangle 5 cm by 3.5 cm, but with a bite taken out, but in this case, it's stepped, so perimeter is larger.

Our calculation gives 17.5 cm.

Let me add again:

Segments:
- Bottom: 5
- Right low up: 2
- Right mid left: 1.5
- Right up up: 1.5
- Top left: 2.5
- Left down: 2.5
- Left mid right: 1.5
- Left down down: 1

Sum: 5+2=7; 7+1.5=8.5; 8.5+1.5=10; 10+2.5=12.5; 12.5+2.5=15; 15+1.5=16.5; 16.5+1=17.5 cm

Yes.

So perimeter for Shape 4 = 17.5 cm

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Final Answers:

Shape 1: 52 cm
Shape 2: 94 mm
Shape 3: 10.5 m
Shape 4: 17.5 cm

Final Answer:
1) 52
2) 94
3) 10.5
4) 17.5