Perimeter Shape Problems Worksheet - Free Printable

Let's solve each perimeter problem step by step. The perimeter of a shape is the total length around the outside, found by adding up all the side lengths.

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1. Square (23 mm sides)

All four sides are equal.
$$
P = 4 \times 23\,\text{mm} = 92\,\text{mm}
$$

✔ Answer: 92 mm

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2. Pentagon with sides: 14 in, 12 in, 11 in, 14 in, 12 in

Add all sides:
$$
14 + 12 + 11 + 14 + 12 = 63\,\text{in}
$$

✔ Answer: 63 in

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3. Triangle (all sides not labeled — but one side is 27 ft)

Wait — only one side is labeled? That’s unusual. But looking closely, it seems like it might be an equilateral triangle, since only one side is shown and it's drawn symmetrically. However, without more info, we can't assume that.

But wait — actually, this looks like a scalene triangle, but only one side is given. That can’t be right unless the other two are missing.

Wait — perhaps it's a regular triangle or there's a mistake?

No — upon closer inspection, the triangle has only one side labeled: 27 ft. But for perimeter, we need all three sides.

Hmm — unless it's an equilateral triangle, then all sides are 27 ft.

But the drawing doesn’t suggest that clearly. Let's recheck.

Actually, in many such worksheets, if only one side is labeled on a triangle and it's drawn as equilateral, it's often assumed to be regular.

But here, no indication. So this might be a typo, or maybe it's meant to be isosceles?

Alternatively, perhaps it's a right triangle? No angles or other sides are labeled.

Wait — perhaps it's not possible to compute without more data?

But let's look at the image again: the triangle has only one side labeled: 27 ft.

That’s insufficient unless it's implied to be equilateral.

But in most cases like this, if only one side is given, and it's a triangle with no other markings, it’s likely equilateral.

So assuming it's equilateral:

$$
P = 3 \times 27\,\text{ft} = 81\,\text{ft}
$$

✔ Answer: 81 ft *(assuming equilateral)*

> ⚠️ Note: This assumption may be necessary due to missing labels.

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4. Rectangle: 145 m (length), 72 m (width)

Opposite sides are equal:
$$
P = 2 \times (145 + 72) = 2 \times 217 = 434\,\text{m}
$$

✔ Answer: 434 m

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5. Irregular Pentagon: 35 cm, 31 cm, 46 cm, 26 cm, 13 cm, 30 cm? Wait — count the sides.

Looking at the figure:
Sides labeled:
- 35 cm
- 31 cm
- 46 cm
- 26 cm
- 13 cm
- 30 cm

Wait — that’s six sides? But it looks like a pentagon.

Wait — let’s trace:
- Top: 35 cm
- Right side: 31 cm
- Bottom right: 46 cm
- Bottom left: 26 cm
- Left side: 13 cm
- Then back up: 30 cm?

Wait — yes, it's a hexagon! Six sides.

List them:
- 35 cm
- 31 cm
- 46 cm
- 26 cm
- 13 cm
- 30 cm

Now add:
$$
35 + 31 = 66 \\
66 + 46 = 112 \\
112 + 26 = 138 \\
138 + 13 = 151 \\
151 + 30 = 181\,\text{cm}
$$

✔ Answer: 181 cm

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6. Right Triangle: 95 yds, 206 yds, 246 yds

Check if it's a right triangle: use Pythagorean theorem?
$$
95^2 + 206^2 = ?\quad 246^2
$$
$$
95^2 = 9025,\quad 206^2 = 42436,\quad \text{Sum} = 51461 \\
246^2 = 60516 → Not equal
$$
Not a right triangle? But it looks like one.

Wait — maybe it's just a triangle with all three sides labeled.

So perimeter:
$$
95 + 206 + 246 = 547\,\text{yds}
$$

✔ Answer: 547 yds

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7. Rhombus (diamond): 3.5 km per side

All four sides equal:
$$
P = 4 \times 3.5 = 14\,\text{km}
$$

✔ Answer: 14 km

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8. Irregular Shape (like a "U" or "C")

Sides:
- Left: 56 mi
- Bottom: 82 mi
- Right: 63 mi
- Top: 45 mi + 45 mi (two segments)

So total:
$$
56 + 82 + 63 + 45 + 45 = ?
$$
$$
56 + 82 = 138 \\
138 + 63 = 201 \\
201 + 45 = 246 \\
246 + 45 = 291\,\text{mi}
$$

✔ Answer: 291 mi

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9. Arrow-shaped figure

We have:
- Horizontal top: 1,200 mm
- Vertical side: 400 mm
- Diagonal: 750 mm
- But also, the arrow has a base — look at the bottom part.

Wait — the figure is a rectangle with a triangle on the right.

Wait — actually, it’s shaped like an arrow pointing right.

Break it down:
- Top horizontal: 1,200 mm
- Right vertical: 400 mm
- Diagonal: 750 mm
- But we must go around the whole shape.

Trace the outer edges:
1. Top: 1,200 mm
2. Right side: from top to bottom of the arrowhead? No — it's a triangle on the end.

Wait — the shape is:
- A rectangle (left part)
- With a triangle attached on the right (arrowhead)

But we’re to find outer perimeter.

So:
- Top: 1,200 mm
- Right side of rectangle: 400 mm (but not full — wait, the arrowhead extends)

Wait — better to list all outer edges:

From the diagram:
- Top edge: 1,200 mm
- Right side: 400 mm (vertical)
- Then diagonal: 750 mm (to the tip)
- Then back down: another 750 mm? No — it's a triangle.

Wait — the triangle has:
- One leg: 400 mm (vertical)
- Hypotenuse: 750 mm
- And base: ?

Wait — actually, the arrowhead has:
- Vertical side: 400 mm
- Slanted side: 750 mm
- But the other slanted side is also 750 mm? Or is it symmetric?

Yes — it's symmetric. So both sides of the triangle are 750 mm.

But the base of the triangle is not part of the perimeter — it's internal?

Wait — no — the arrowhead has two slanted sides (750 mm each), and the bottom of the triangle is connected to the rectangle.

But the rectangle has:
- Width: 1,200 mm
- Height: 400 mm

But the top of the rectangle is 1,200 mm, and the side is 400 mm.

Then the arrowhead is attached to the right end.

So the outer perimeter includes:
- Top: 1,200 mm
- Right side of rectangle: 400 mm (down)
- Then two slanted sides of the arrowhead: 750 mm and 750 mm
- Then back along the bottom? Wait — no — the bottom of the arrowhead connects to the rectangle.

Wait — actually, the entire shape has:
- Top: 1,200 mm
- Right side: from top to bottom of rectangle: 400 mm
- Then from bottom of rectangle, goes diagonally up-right to tip: 750 mm
- Then from tip, diagonally down-left to bottom of rectangle: 750 mm
- Then from bottom of rectangle, left along the bottom: 1,200 mm
- Then up the left side: 400 mm

Wait — but the bottom of the rectangle is not exposed? No — it is.

Wait — no — the shape is closed.

Let’s trace:
1. Start at top-left corner.
2. Go right: 1,200 mm → top
3. Down right side: 400 mm → bottom-right of rectangle
4. Then go diagonally up to tip: 750 mm
5. Then go diagonally down to bottom of arrowhead: 750 mm
6. Then go left along bottom: 1,200 mm → back to start?

Wait — no — the bottom of the arrowhead is not aligned with the rectangle’s bottom.

Wait — actually, the arrowhead is attached to the right side of the rectangle, so the bottom of the arrowhead is below the rectangle.

So the full perimeter is:
- Top: 1,200 mm
- Right side of rectangle: 400 mm (from top to bottom)
- Then from bottom of rectangle, go diagonally up to tip: 750 mm
- Then from tip, go diagonally down to bottom of arrowhead: 750 mm
- Then from bottom of arrowhead, go left along the bottom: 1,200 mm
- Then up the left side: 400 mm

Wait — but now we’re going from bottom of arrowhead to left — but the bottom of the rectangle is already covered?

Wait — confusion.

Better: The shape has:
- A rectangle: width = 1,200 mm, height = 400 mm
- Attached to the right side of the rectangle is a triangle with:
- Base = 400 mm (same as height of rectangle)
- Two equal sides = 750 mm

So the perimeter includes:
- Top of rectangle: 1,200 mm
- Right side of rectangle: 400 mm
- Then from bottom of rectangle, go up the triangle: 750 mm
- Then from tip, go down: 750 mm
- Then from bottom of triangle, go left along the bottom: 1,200 mm
- Then up the left side: 400 mm

Wait — but the bottom of the rectangle is not included? No — it is.

But the triangle is attached to the right side of the rectangle, so the right side of the rectangle is internal and not part of the perimeter?

Ah! That’s key.

The right side of the rectangle is shared with the triangle, so it's not part of the outer perimeter.

So correct tracing:

Start at top-left:
1. Top: 1,200 mm → to top-right
2. But instead of going down the right side, we go into the triangle — but the triangle is attached.

So the outer path:
- Top: 1,200 mm
- Then down the left side of the triangle? No — the triangle is on the right.

Wait — better:

The shape is:
- Rectangle: 1,200 mm wide, 400 mm high
- On the right side, a triangle is attached: its base is 400 mm (same as rectangle height), and two sides are 750 mm each.

So the outer perimeter consists of:
- Top of rectangle: 1,200 mm
- Right side of rectangle: not included — it's covered by triangle
- Instead, from top-right corner, go up the triangle’s right side? No — triangle is attached to the right side, so the triangle has:
- Base: 400 mm (along the right side of rectangle)
- Two slanted sides: 750 mm each

So the outer path:
1. Top: 1,200 mm
2. From top-right, go up the triangle’s right side: 750 mm
3. From tip, go down the left side of triangle: 750 mm
4. From bottom of triangle, go left along bottom: 1,200 mm
5. Up left side: 400 mm

Wait — but the bottom of the triangle is below the rectangle? Or level?

Actually, the triangle is attached to the right side, so its base is horizontal, same as rectangle's right side.

So the triangle has:
- Base: 400 mm (aligned with rectangle's right side)
- Two equal sides: 750 mm

So the outer perimeter:
- Top: 1,200 mm
- Then from top-right, go along the triangle’s right side: 750 mm
- Then from tip, go along the triangle’s left side: 750 mm
- Then from bottom of triangle, go left along bottom: 1,200 mm
- Then up left side: 400 mm

But what about the right side of the rectangle? It's internal — covered by triangle base — so not part of perimeter.

So total:
- Top: 1,200
- Right slant: 750
- Left slant: 750
- Bottom: 1,200
- Left side: 400

Wait — but the bottom is 1,200 mm, but the triangle is on the right, so the bottom of the rectangle is still exposed.

Yes.

So sum:
$$
1,200 + 750 + 750 + 1,200 + 400 = ?
$$
$$
1,200 + 750 = 1,950 \\
+750 = 2,700 \\
+1,200 = 3,900 \\
+400 = 4,300\,\text{mm}
$$

But wait — the bottom is only 1,200 mm, but the triangle is on the right, so the bottom of the shape is still 1,200 mm long.

Yes.

So total perimeter: 4,300 mm

✔ Answer: 4,300 mm

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10. Rectangle: 66 in (width), 140 in (height)

$$
P = 2 \times (66 + 140) = 2 \times 206 = 412\,\text{in}
$$

✔ Answer: 412 in

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✔ Final Answers:

| Problem | Perimeter |
|--------|-----------|
| 1 | 92 mm |
| 2 | 63 in |
| 3 | 81 ft |
| 4 | 434 m |
| 5 | 181 cm |
| 6 | 547 yds |
| 7 | 14 km |
| 8 | 291 mi |
| 9 | 4,300 mm |
| 10 | 412 in |

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Let me know if you'd like this formatted as a printable answer sheet!