Perimeter - Worksheet | Maths Year 3 - Free Printable

Let’s solve each shape one by one. Remember: Perimeter = add up all the sides.

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Shape 1:
It’s a square with all sides = 6 cm.
So, perimeter = 6 + 6 + 6 + 6 = 24 cm

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Shape 2:
Rectangle: two sides are 6 m, two sides are 1 m.
Perimeter = 6 + 1 + 6 + 1 = 14 m

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Shape 3:
Trapezoid with sides: 7 cm, 4 cm, 7 cm, 10 cm.
Add them: 7 + 4 + 7 + 10 =
7+4=11; 11+7=18; 18+10= 28 cm

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Shape 4:
This is an L-shaped figure. Let’s list all outer sides:

Top: 8 cm
Right top vertical: 3 cm
Middle horizontal right: 4 cm
Right bottom vertical: 4 cm
Bottom: 12 cm
Left side: 7 cm

Wait — let’s check if we missed any? Actually, look at the left side: it’s 7 cm total. The top part goes down 3 cm, then over 4 cm, then down 4 cm — that adds to 7 cm (3+4), so the left side matches.

But we must include every outer edge:

Start from top-left and go clockwise:

- Top: 8 cm
- Down 3 cm
- Right 4 cm
- Down 4 cm
- Bottom: 12 cm
- Left: 7 cm ← but wait! From bottom-left corner going up, we have 7 cm, which covers the whole left side. But actually, when you go around, after the bottom 12 cm, you go up the left side 7 cm — that’s correct.

BUT — hold on! When you go from top-right down 3 cm, then right 4 cm, then down 4 cm — that means the total height on the right is 3+4=7 cm, same as left. So no missing parts.

Now add: 8 + 3 + 4 + 4 + 12 + 7 =
8+3=11; 11+4=15; 15+4=19; 19+12=31; 31+7= 38 cm

Wait — let me double-check by another way.

Alternative method: Imagine this as a big rectangle minus a small rectangle, but for perimeter, sometimes it’s easier to trace the outline.

Actually, looking again: the top is 8 cm, then down 3 cm, then right 4 cm, then down 4 cm, then left along bottom 12 cm, then up 7 cm on left.

But when you go up 7 cm on the left, you’re back to start? No — because the top is only 8 cm, but the bottom is 12 cm. That means there’s a “step” on the left too? Wait, no — in the diagram, the left side is straight 7 cm. So how does the bottom become 12 cm?

Ah — I think I made a mistake. Let me re-express the shape:

The full width at bottom is 12 cm. At top, it’s 8 cm. So the extra 4 cm is on the right side sticking out? Actually, looking at the labels:

From top-left:

- Go right 8 cm → top edge
- Go down 3 cm → first vertical drop
- Go right 4 cm → middle horizontal
- Go down 4 cm → second vertical drop
- Go left 12 cm → bottom edge
- Go up 7 cm → left edge back to start

But if you go left 12 cm on bottom, and started at top-left, then went right 8 + 4 = 12 cm total on top/middle, then yes, bottom 12 cm brings you back under the starting point? Not exactly — because the left side is 7 cm tall, and you went down 3 + 4 = 7 cm on the right, so vertically it matches.

Horizontally: top path is 8 + 4 = 12 cm, bottom is 12 cm — so it closes.

So sides are: 8, 3, 4, 4, 12, 7 → sum is 8+3=11, +4=15, +4=19, +12=31, +7=38 cm.

Yes, 38 cm is correct.

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Shape 5:
This is a rectangle with a notch cut out at the bottom.

Outer dimensions: top = 12 cm, left = 8 cm, right = 8 cm.

At the bottom, instead of a straight line, there’s a U-shape cut out.

Label the sides going clockwise from top-left:

- Top: 12 cm
- Right side: 8 cm
- Bottom-right horizontal: 5 cm (given)
- Up inside: 4 cm
- Across the notch: 3 cm
- Down inside: 4 cm
- Bottom-left horizontal: 4 cm
- Left side: 8 cm ← but wait, we already used the left side? No — we started at top-left, went right, down, etc., and now we need to close the shape.

Actually, let's list all segments in order:

Start at top-left corner:

1. Right along top: 12 cm
2. Down right side: 8 cm
3. Left along bottom-right segment: 5 cm
4. Up inner right: 4 cm
5. Left across notch: 3 cm
6. Down inner left: 4 cm
7. Left along bottom-left segment: 4 cm
8. Up left side: 8 cm ← but this would overshoot because we’re already at the bottom-left corner? Wait, no.

After step 7, we are at the bottom-left corner of the main rectangle. Then we go up the left side 8 cm to return to start.

But let’s verify the horizontal lengths:

Total bottom should be: left segment (4 cm) + notch width (3 cm) + right segment (5 cm) = 4+3+5=12 cm — matches top. Good.

Verticals: left and right sides are both 8 cm. The inner ups and downs are 4 cm each — they cancel out in terms of net displacement, but for perimeter, we count them.

So adding all sides:

12 (top)
+ 8 (right)
+ 5 (bottom-right)
+ 4 (up inner right)
+ 3 (across notch)
+ 4 (down inner left)
+ 4 (bottom-left)
+ 8 (left side) ← wait, but if we go up the left side 8 cm, that’s correct to close.

But let’s add: 12 + 8 = 20; +5=25; +4=29; +3=32; +4=36; +4=40; +8=48 cm.

Is that right? Let me think differently.

Imagine the full rectangle without notch: perimeter would be 2*(12+8)=40 cm.

But we cut out a notch: we removed a 3 cm wide by 4 cm deep rectangle from the bottom.

When you cut out a notch like this, you remove the bottom segment of 3 cm, but you add three new sides: two verticals of 4 cm each and one horizontal of 3 cm on top of the notch.

Original bottom was 12 cm. After cutting notch, the bottom becomes two pieces: 4 cm and 5 cm, totaling 9 cm, plus the notch adds 4 + 3 + 4 = 11 cm of new edges? Wait no.

Better: original perimeter: 40 cm.

Cutting the notch: you remove the 3 cm segment from the bottom (so subtract 3 cm), but you add the two sides of the notch (each 4 cm) and the top of the notch (3 cm). So net change: -3 + 4 + 3 + 4 = +8 cm.

So new perimeter = 40 + 8 = 48 cm. Same as before.

Yes, 48 cm

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Shape 6:
This is a complex shape with steps on all sides. Let’s trace the perimeter carefully.

Going clockwise from top-left:

- Top: 10 cm
- Down right-top: 2 cm
- Right: 2 cm
- Down: 5 cm
- Left: 2 cm
- Down: 2 cm
- Bottom: 10 cm
- Up left-bottom: 2 cm
- Left: 2 cm
- Up: 5 cm
- Right: 2 cm
- Up: 2 cm ← back to start? Let’s see.

Actually, let’s list all labeled segments:

Top: 10 cm
Then on right side: from top-right, down 2 cm, then right 2 cm? Wait, no — looking at the diagram:

From top-left:

1. Right 10 cm (top)
2. Down 2 cm (first step down on right)
3. Right 2 cm? No — actually, after down 2 cm, it goes left? Wait, the label says "2 cm" pointing right from the top-right corner? I think I need to interpret the arrows.

Looking at the diagram description:

It says:

Top: 10 cm

On the right side: from top, down 2 cm, then the next segment is labeled "2 cm" going right? That doesn’t make sense. Probably, the "2 cm" labels are for the step sizes.

Actually, standard interpretation for such shapes: it’s symmetric.

Notice: top and bottom are both 10 cm.

Left and right have similar steps.

Let me try to calculate by grouping.

Another way: this shape can be seen as a large rectangle with indentations, but perhaps easiest to add all given sides.

List all outer edges as per labels:

Starting from top-left, going clockwise:

- Top: 10 cm
- Then down: 2 cm (labeled on right-top)
- Then right: 2 cm? Wait, the label "2 cm" is shown pointing to the right from the top-right area — probably meaning the horizontal step is 2 cm.

Actually, looking at the text: "2 cm" appears multiple times.

Perhaps better to note that the total width is 10 cm at top and bottom.

The height: on left side, from top to bottom: 2 cm (down) + 5 cm (down) + 2 cm (down) = 9 cm? But on right side same: 2+5+2=9 cm.

But let's trace:

Assume we start at top-left corner.

Move right 10 cm → top edge.

Then move down 2 cm → first vertical on right.

Then move left 2 cm? No — the diagram likely has steps inward.

Standard problem: this is a rectangle with notches on all sides, but actually, it's like a frame.

Notice that all the "step" sizes are given.

Let me add all the segments that are labeled:

There are:

- Two horizontal tops/bottoms: 10 cm each → 20 cm
- On left side: three vertical segments: 2 cm, 5 cm, 2 cm → total 9 cm
- On right side: similarly 2 cm, 5 cm, 2 cm → 9 cm
- Plus the horizontal steps: on top-right, there's a 2 cm horizontal? And on bottom-left, etc.

Actually, looking closely, the shape has:

At the top: 10 cm

Then on the right, it steps down 2 cm, then steps left 2 cm? But the label "2 cm" is placed near the step.

I recall that in such problems, the perimeter can be found by noting that the total horizontal movement equals twice the width, and vertical equals twice the height, but with steps, it might be different.

Alternative approach: imagine walking around the shape. Every time you go right or left, the total rightward distance must equal total leftward, and same for up/down.

But for perimeter, we just sum all sides.

Let me list all sides based on common interpretation of such diagrams:

Typically, for shape 6:

- Top: 10 cm
- Right-top vertical: 2 cm
- Right-middle horizontal: 2 cm (inward)
- Right-bottom vertical: 5 cm
- Bottom-right horizontal: 2 cm (outward?) — this is confusing.

Perhaps the "2 cm" labels indicate the size of the steps.

Another idea: the overall bounding box is 10 cm wide and (2+5+2)=9 cm high.

But with steps, the perimeter increases.

Let's count the segments as drawn:

From the diagram description, there are 12 segments:

1. Top: 10 cm
2. Down on right: 2 cm
3. Left on right-top: 2 cm (this is the step inward)
4. Down on right-middle: 5 cm
5. Left on right-bottom: 2 cm (another step inward? But then it would be less than 10 cm)

I think I found a better way. Notice that the shape is symmetric, and the total perimeter can be calculated by adding all the outer paths.

Let me try this: start at top-left.

- Move right 10 cm (top)
- Move down 2 cm
- Move left 2 cm (this is the first step on the right side)
- Move down 5 cm
- Move left 2 cm (second step on right)
- Move down 2 cm? No, after moving left 2 cm, you are at the bottom-right corner of the inner part, but then you need to go to the bottom.

Actually, after moving down 5 cm, you are at a point, then you move left 2 cm, then down 2 cm to reach the bottom level? But the bottom is labeled 10 cm.

Perhaps the bottom is from left to right 10 cm, but with steps.

Let's look for a pattern. In many textbooks, for such a shape, the perimeter is the same as the bounding rectangle if the steps are compensated, but here it's not.

Let's calculate the total length by considering that each "step" adds extra length.

Bounding rectangle: width 10 cm, height 2+5+2=9 cm, so perimeter 2*(10+9)=38 cm.

But when you have steps, for each step inward, you add twice the depth of the step.

For example, on the right side, there are two steps: one of 2 cm depth (horizontal), and one of 2 cm depth, but they are at different heights.

Actually, for each indentation, you add 2 times the depth for the two sides.

In this case, on the top-right, there is a step down 2 cm and left 2 cm — this adds 2*2 = 4 cm extra compared to a straight line? Let's think.

If it were a straight rectangle, from top-right to bottom-right is 9 cm down.

Here, you go down 2 cm, left 2 cm, down 5 cm, left 2 cm, down 2 cm — so the path is longer.

The direct vertical is 9 cm, but the actual path is 2 + 2 + 5 + 2 + 2 = 13 cm? That can't be right because the last "down 2 cm" might not be there.

I think I need to accept that the intended solution is to add all labeled sides.

Let me list all the numbers given in the diagram for shape 6:

- Top: 10 cm
- Bottom: 10 cm
- Left side: 5 cm (middle), and 2 cm (top and bottom) — but also there are horizontal steps.

The labels are:

On the left: from top, down 2 cm, then the next segment is labeled "2 cm" pointing right? This is ambiguous.

Perhaps the "2 cm" are the lengths of the horizontal steps.

Let me assume the following based on standard problems:

The shape has:

- Top: 10 cm
- Then on the right: down 2 cm, then left 2 cm, then down 5 cm, then left 2 cm, then down 2 cm — but then the bottom would be shorter.

After down 2 cm (first), left 2 cm, down 5 cm, left 2 cm, down 2 cm, then you are at the bottom-right corner, but the bottom is labeled 10 cm, which suggests that from there you go left 10 cm, but that would overlap.

I recall that in some versions, this shape has a perimeter of 48 cm or something.

Let's try to calculate the total horizontal and vertical components.

Total horizontal distance traveled: when you go around, the sum of all rightward moves equals sum of all leftward moves, and each is equal to the width of the shape.

Similarly for vertical.

For this shape, the maximum width is 10 cm, so total rightward + leftward = 2 * 10 = 20 cm.

Maximum height is 2+5+2=9 cm, so total upward + downward = 2 * 9 = 18 cm.

Therefore, perimeter = 20 + 18 = 38 cm.

Is that correct? Only if the shape is rectilinear and convex, but here it has indentations, so the total path may be longer.

In a rectilinear polygon, the perimeter is indeed 2*(width + height) if it's monotonic, but with indentations, it can be more.

For example, if you have a rectangle with a bite taken out, perimeter increases.

In this case, let's consider the steps.

Suppose the shape is like a rectangle 10 cm by 9 cm, but with two notches on the right side and two on the left side.

Each notch of depth d adds 2d to the perimeter.

Here, on the right side, there are two notches: one of 2 cm depth (horizontal), and one of 2 cm depth, but they are separate.

Actually, looking at the diagram, it seems that on each side, there are steps that make the perimeter larger.

Let me search for a different strategy. Let's add all the segments as labeled in the image.

From the user's description, the labels are:

For shape 6:

- Top: 10 cm
- On the right: from top, down 2 cm, then the next label is "2 cm" which is probably the horizontal segment to the left, then down 5 cm, then "2 cm" horizontal to the left, then down 2 cm? But then the bottom is 10 cm, which would require that from the bottom-right, you go left 10 cm, but if you've already moved left 2+2=4 cm on the right side, then the bottom should be 10 - 4 = 6 cm, but it's labeled 10 cm, so contradiction.

Unless the "2 cm" on the right are not additional, but part of the structure.

Perhaps the "2 cm" labels are for the vertical segments on the sides.

Let's read the user's input: "6. ... 2 cm, 2 cm, 2 cm, 5 cm, 2 cm, 2 cm, 10 cm, 2 cm, 2 cm, 2 cm, 5 cm, 2 cm" — but it's messy.

Another idea: in many such problems, the perimeter is calculated by noting that the total length of all horizontal segments is 2 * 10 = 20 cm (since top and bottom are 10 cm, and the internal horizontals cancel out in pairs, but for perimeter, we count all).

Actually, for a closed shape, the sum of all horizontal segments (left and right) must be even, but for perimeter, we sum absolute values.

Let's assume that the shape has the following sides in order:

Start at top-left:

1. Right 10 cm (top)
2. Down 2 cm
3. Left 2 cm (first step)
4. Down 5 cm
5. Left 2 cm (second step)
6. Down 2 cm — but then you are at the bottom-right corner, and the bottom is from here to bottom-left, which should be 10 cm, but if you've moved left 2+2=4 cm from the right, then the distance to left is 10 - 4 = 6 cm, but the bottom is labeled 10 cm, so perhaps the bottom is 10 cm from left to right, meaning that after step 5, you are not at the bottom yet.

Perhaps after step 5 (left 2 cm), you are at a point, then you go down 2 cm to the bottom level, then left 10 cm to bottom-left, then up 2 cm, then right 2 cm, then up 5 cm, then right 2 cm, then up 2 cm to start.

Let's try that:

Segments:

1. Top: 10 cm right
2. Down 2 cm
3. Left 2 cm
4. Down 5 cm
5. Left 2 cm
6. Down 2 cm -- now at bottom-right corner? But then bottom should be from here to bottom-left, which is 10 cm left, but if you've moved left 2+2=4 cm from the right edge, then the x-coordinate is 10 - 4 = 6 cm from left, so to go to left edge, you need to go left 6 cm, but the bottom is labeled 10 cm, so not matching.

Unless the bottom is 10 cm, so from bottom-right to bottom-left is 10 cm left.

So perhaps the steps are on the inside.

I think I found the error. In the diagram, the "2 cm" on the right are not additional left moves, but rather the size of the steps, and the bottom is still 10 cm.

Let's calculate the total length by adding all unique segments.

Perhaps the shape is composed of:

- Top: 10 cm
- Right side: consists of three vertical segments: 2 cm, 5 cm, 2 cm, but with horizontal connections.

Actually, for such a shape, the perimeter can be calculated as follows:

The total horizontal contribution: the top and bottom are each 10 cm, and there are additional horizontal segments on the sides.

On the right side, there are two horizontal segments of 2 cm each (the steps), and on the left side, two horizontal segments of 2 cm each.

Similarly for vertical.

Let's list all segments:

Horizontal segments:
- Top: 10 cm
- Bottom: 10 cm
- On right side: two horizontal steps: each 2 cm, so 4 cm
- On left side: two horizontal steps: each 2 cm, so 4 cm
Total horizontal: 10+10+4+4 = 28 cm

Vertical segments:
- On right side: three vertical segments: 2 cm, 5 cm, 2 cm = 9 cm
- On left side: three vertical segments: 2 cm, 5 cm, 2 cm = 9 cm
Total vertical: 9+9 = 18 cm

Perimeter = 28 + 18 = 46 cm

But is that correct? Let's see if it makes sense.

Another way: the shape has a width of 10 cm, but with steps, the effective width for horizontal travel is more.

Perhaps the correct answer is 48 cm, as in some sources.

Let's try to simulate the path.

Start at top-left corner A.

- Move right 10 cm to B (top-right)
- Move down 2 cm to C
- Move left 2 cm to D (this is the first step inward)
- Move down 5 cm to E
- Move left 2 cm to F (second step inward)
- Move down 2 cm to G (now at bottom-right corner of the inner part)
- But the bottom is labeled 10 cm, so from G, move left 10 cm to H (bottom-left) — but if G is at x=10-2-2=6 cm from left (assuming A is at x=0), then moving left 10 cm would take you to x= -4, which is impossible.

So that can't be.

Unless the bottom is from the leftmost to rightmost, but in this case, the rightmost is at x=10, leftmost at x=0, so bottom should be from x=0 to x=10 at y= min.

After moving down from A(0,9) say, to B(10,9), down to C(10,7), left to D(8,7), down to E(8,2), left to F(6,2), down to G(6,0), then to go to bottom-left, you need to go left to (0,0), which is 6 cm, but the bottom is labeled 10 cm, so perhaps the bottom is from (0,0) to (10,0), but G is at (6,0), so you need to go right to (10,0)? That doesn't make sense.

I think there's a misinterpretation.

Let me look for a standard solution or rethink.

Perhaps the "2 cm" on the right are not left moves, but the vertical segments are labeled, and the horizontal are implied.

Another idea: in the diagram, the shape is symmetric, and the total perimeter is 2 * (10 + 9) + 2*2*2 = 38 + 8 = 46 cm, since there are four steps of 2 cm each that add extra length.

Each "corner" step adds 2* depth, but here the steps are on the sides.

Let's calculate the difference from the bounding rectangle.

Bounding rectangle: 10 cm wide, 9 cm high, perimeter 2*(10+9) = 38 cm.

Now, on the right side, instead of a straight 9 cm down, you have a path that goes down 2, left 2, down 5, left 2, down 2 — so the length of this path is 2+2+5+2+2 = 13 cm, while the straight line is 9 cm, so extra 4 cm.

Similarly on the left side, same thing: extra 4 cm.

So total extra 8 cm, so perimeter = 38 + 8 = 46 cm.

Yes, that makes sense.

For the left side: from top-left, instead of down 9 cm, you go down 2, right 2, down 5, right 2, down 2 — length 2+2+5+2+2=13 cm, extra 4 cm.

So total perimeter = 38 + 4 + 4 = 46 cm.

And the top and bottom are still 10 cm each, but in the bounding rectangle, top and bottom are included, and the sides are replaced by longer paths.

In the bounding rectangle, the right side is 9 cm, but here it's 13 cm, so +4 cm, similarly left side +4 cm, so total +8 cm, so 38 + 8 = 46 cm.

Yes.

To confirm, let's add all segments:

- Top: 10 cm
- Right side path: down 2, left 2, down 5, left 2, down 2 — but the "left 2" are horizontal, so for the right side, the segments are: vertical 2, horizontal 2 (left), vertical 5, horizontal 2 (left), vertical 2 — so 5 segments.

Similarly for left side: from bottom-left, up 2, right 2, up 5, right 2, up 2 — but when you go around, after bottom, you go up the left side.

Let's define the path:

Start at top-left (0,9)

1. Right to (10,9) : 10 cm
2. Down to (10,7) : 2 cm
3. Left to (8,7) : 2 cm
4. Down to (8,2) : 5 cm
5. Left to (6,2) : 2 cm
6. Down to (6,0) : 2 cm -- now at (6,0)
7. Left to (0,0) : 6 cm? But the bottom is labeled 10 cm, so perhaps from (6,0) to (0,0) is 6 cm, but the label says 10 cm for bottom, so maybe the bottom is from (0,0) to (10,0), but we are at (6,0), so we need to go to (0,0) or to (10,0)?

This is inconsistent.

Unless the bottom is from the leftmost to rightmost, but in this case, the rightmost is at x=10, leftmost at x=0, so bottom should be from (0,0) to (10,0), but after step 6, we are at (6,0), so to close the shape, we need to go to (0,0) or to (10,0)? Neither makes sense.

Perhaps after step 6, we are at the bottom-right of the inner part, but the bottom of the shape is from (0,0) to (10,0), so from (6,0) we go left to (0,0) : 6 cm, then up to (0,2) : 2 cm, then right to (2,2) : 2 cm, then up to (2,7) : 5 cm, then right to (4,7) : 2 cm, then up to (4,9) : 2 cm, then right to (10,9) : 6 cm? But that would be overlapping.

I think the only logical way is to assume that the "bottom 10 cm" is the full bottom, and the steps are above it.

Perhaps the shape is:

- Top: 10 cm
- Then on the right: down 2 cm, then the next segment is not left, but the "2 cm" is the length of the vertical segment below, but it's labeled as horizontal.

I recall that in some worksheets, for shape 6, the perimeter is 48 cm.

Let me calculate as follows: add all the numbers given in the diagram for shape 6.

From the user's text: "6. ... 2 cm, 2 cm, 2 cm, 5 cm, 2 cm, 2 cm, 10 cm, 2 cm, 2 cm, 2 cm, 5 cm, 2 cm" — but it's not clear.

Perhaps there are 12 segments:

Let's list them as per common practice:

1. Top: 10 cm
2. Right-top vertical: 2 cm
3. Right-top horizontal: 2 cm (inward)
4. Right-middle vertical: 5 cm
5. Right-bottom horizontal: 2 cm (inward)
6. Right-bottom vertical: 2 cm
7. Bottom: 10 cm
8. Left-bottom vertical: 2 cm
9. Left-bottom horizontal: 2 cm (outward)
10. Left-middle vertical: 5 cm
11. Left-top horizontal: 2 cm (outward)
12. Left-top vertical: 2 cm

Then sum: 10+2+2+5+2+2+10+2+2+5+2+2 = let's calculate: 10+10=20, 2+2+2+2+2+2+2+2=16, 5+5=10, so 20+16+10=46 cm.

Same as before.

And this makes sense because the horizontal segments: top 10, bottom 10, and on right: two 2 cm inward, on left: two 2 cm outward, but in the path, when you go inward on right, you later go outward on left, but for perimeter, you count all.

In this list, the segments are all outer edges.

So perimeter = 46 cm.

I think that's correct.

So for shape 6: 46 cm

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Now, let's summarize all answers:

1. 24 cm
2. 14 m
3. 28 cm
4. 38 cm
5. 48 cm
6. 46 cm

Final Answer:
1. 24
2. 14
3. 28
4. 38
5. 48
6. 46