Perimeter calculation worksheet featuring six different geometric shapes with given dimensions.

Let’s solve each problem step by step. Perimeter is the total distance around the outside of a shape — you add up all the side lengths.

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1. Square with all sides 6 cm

- All 4 sides are equal: 6 cm each.
- Perimeter = 6 + 6 + 6 + 6 = 24 cm

✔ Answer: 24 cm

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2. Rectangle with length 6 m and width 1 m

- Opposite sides are equal.
- Sides: 6 m, 1 m, 6 m, 1 m
- Perimeter = 6 + 1 + 6 + 1 = 14 m

✔ Answer: 14 m

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3. Trapezoid with sides 4 cm, 7 cm, 10 cm, 7 cm

- Just add all the sides: 4 + 7 + 10 + 7
- = 4 + 7 = 11; 11 + 10 = 21; 21 + 7 = 28 cm

✔ Answer: 28 cm

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4. Irregular shape (like a rectangle with a step)

Label the sides as given:

- Top: 8 cm
- Right top step: 3 cm down
- Step horizontal: 4 cm right
- Step vertical down: 4 cm
- Bottom: 12 cm
- Left side: 7 cm

But we need to find all outer edges.

Let’s trace the perimeter clockwise:

- Start at top-left:
- → Right along top: 8 cm
- ↓ Down right side of step: 3 cm
- → Right along step: 4 cm
- ↓ Down to bottom: 4 cm
- ← Left along bottom: 12 cm
- ↑ Up left side: 7 cm

Wait — that’s only 5 sides? We missed the left part above the step.

Actually, the total height on the left is 7 cm. The step goes down 3 cm and then another 4 cm, so 3 + 4 = 7 cm — that matches.

But what about the top-left to top-right? It’s 8 cm, and the bottom is 12 cm. So the “missing” part on the top is accounted for by the step.

Better way: Think of it as a big rectangle with a notch, but since we’re measuring outer edge, we just add all visible sides.

List all outer segments:

- Top horizontal: 8 cm
- Right vertical (step part): 3 cm
- Step horizontal: 4 cm
- Lower right vertical: 4 cm
- Bottom horizontal: 12 cm
- Left vertical: 7 cm

Now — is that all? Let’s check if we’ve covered every edge.

Actually, between the top-left corner and the start of the 8 cm top, there’s no gap — so we have:

Total = 8 + 3 + 4 + 4 + 12 + 7 = 38 cm

✔ Answer: 38 cm

*(Alternative method: Imagine stretching the shape into a rectangle. The total width is 12 cm, height 7 cm → 2×(12+7)=38 cm. The step doesn’t change the perimeter because the horizontal and vertical segments added are exactly offset by the missing parts.)*

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5. Shape with a notch in the bottom

Given:

- Top: 12 cm
- Right side: 8 cm
- Bottom right: 5 cm (horizontal)
- Then up 4 cm (vertical)
- Then left 3 cm (horizontal)
- Then down 4 cm (vertical)
- Then left 4 cm (horizontal)
- Left side: 8 cm

Trace perimeter clockwise:

- Top: 12 cm
- Right down: 8 cm
- Bottom right segment: 5 cm
- Up: 4 cm
- Left across notch: 3 cm
- Down: 4 cm
- Left to corner: 4 cm
- Up left side: 8 cm

Add them:

12 + 8 = 20
20 + 5 = 25
25 + 4 = 29
29 + 3 = 32
32 + 4 = 36
36 + 4 = 40
40 + 8 = 48 cm

✔ Answer: 48 cm

*(Note: The notch adds extra perimeter — instead of a straight bottom of 12 cm, we have 5 + 3 + 4 = 12 cm horizontally, but we also add two verticals of 4 cm each, so total perimeter increases by 8 cm compared to a full rectangle. Original rectangle would be 2×(12+8)=40 cm, plus 8 cm from notch = 48 cm.)*

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6. Symmetrical shape with steps on both sides

This looks like a rectangle with two “steps” on left and right.

Given dimensions:

- Top: 10 cm
- Right side: 2 cm down, then 2 cm right, then 5 cm down, then 2 cm left, then 2 cm down → wait, let’s trace carefully.

Actually, label the sides:

Start at top-left:

- → Right: 10 cm (top)
- ↓ Down right side: 2 cm
- → Right: 2 cm (small step out)
- ↓ Down: 5 cm
- ← Left: 2 cm (step back in)
- ↓ Down: 2 cm
- ← Left along bottom: 10 cm
- ↑ Up left side: 2 cm
- → Right: 2 cm (step out)
- ↑ Up: 5 cm
- ← Left: 2 cm (step back in)
- ↑ Up to top: 2 cm

Now list all segments:

Top: 10
Right top down: 2
Right step right: 2
Right down: 5
Right step left: 2
Bottom right down: 2
Bottom: 10
Left up: 2
Left step right: 2
Left up: 5
Left step left: 2
Left top up: 2

Add them:

Group:

Top & bottom: 10 + 10 = 20
Left & right verticals: Each side has 2 + 5 + 2 = 9 cm → 9 × 2 = 18
Steps: Each side has two horizontal steps: 2 cm out and 2 cm back → 4 cm per side → 8 cm total

Wait — better to just add all:

10 (top)
+ 2 (right down)
+ 2 (right step out)
+ 5 (right down)
+ 2 (right step in)
+ 2 (bottom right down)
+ 10 (bottom)
+ 2 (left up)
+ 2 (left step out)
+ 5 (left up)
+ 2 (left step in)
+ 2 (left top up)

Now add:

10 + 2 = 12
+2 = 14
+5 = 19
+2 = 21
+2 = 23
+10 = 33
+2 = 35
+2 = 37
+5 = 42
+2 = 44
+2 = 46 cm

✔ Answer: 46 cm

*(Alternative: Imagine the full outer rectangle would be 10 cm wide and (2+5+2)=9 cm tall → 2×(10+9)=38 cm. But each side has two "bumps" adding 2 cm horizontal each, so 4 cm extra per side → 8 cm total. 38 + 8 = 46 cm.)*

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## ✔ Final Answers:

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

Let me know if you’d like diagrams or further explanation!