Find the perimeter - Grand Prairie Elementary - Free Printable

Let’s solve each perimeter problem step by step. Remember: Perimeter = add up all the side lengths.

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1. Rectangle (38 km, 67 km)
A rectangle has two pairs of equal sides.
So sides are: 38, 67, 38, 67
Add them: 38 + 67 = 105 → 105 + 38 = 143 → 143 + 67 = 210 km

✔ Perimeter = 210 km

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2. Trapezoid (67 cm, 22 cm, 18 cm, 22 cm)
All four sides given: 67, 22, 18, 22
Add: 67 + 22 = 89 → 89 + 18 = 107 → 107 + 22 = 129 cm

✔ Perimeter = 129 cm

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3. Square (23 m)
All 4 sides equal → 23 + 23 + 23 + 23
Or 23 × 4 = 92 m

✔ Perimeter = 92 m

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4. Isosceles Triangle (249 cm, 249 cm, 203 cm)
Two sides same: 249, 249, 203
Add: 249 + 249 = 498 → 498 + 203 = 701 cm

✔ Perimeter = 701 cm

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5. Octagon (Symmetrical) – Sides: 134 km, 23 km, 48 km, 23 km, and opposite sides same?
Wait — it says “Octagon (Symmetrical)” and shows 4 labeled sides: top=134, right-top=23, right-bottom=48, bottom-right=23? Actually, looking at shape — it’s symmetric left/right and top/bottom? But only 4 sides labeled. Let’s assume it’s symmetrical so opposite sides are equal.

Actually, from diagram: it looks like a stretched octagon with:
- Top: 134
- Right upper slant: 23
- Right vertical: 48
- Right lower slant: 23
Then by symmetry, left side mirrors right → so total sides:

Top: 134
Bottom: 134 (same as top)
Right upper: 23 → Left upper: 23
Right vertical: 48 → Left vertical: 48
Right lower: 23 → Left lower: 23

Wait — that’s 8 sides:
134, 23, 48, 23, 134, 23, 48, 23? No — that would be too many.

Actually, standard way: if it’s symmetrical and labeled on one half, we double.

Looking again: the figure is drawn with 8 sides, but only 4 labeled: top=134, right-top=23, right-middle=48, right-bottom=23. Since it’s symmetrical, the left side matches: left-top=23, left-middle=48, left-bottom=23, and bottom=134.

So all 8 sides:
Top: 134
Right-top: 23
Right-middle: 48
Right-bottom: 23
Bottom: 134
Left-bottom: 23
Left-middle: 48
Left-top: 23

Now add:
Group them:
134 + 134 = 268
23 + 23 + 23 + 23 = 92 (four 23s)
48 + 48 = 96
Total: 268 + 92 = 360 → 360 + 96 = 456 km

✔ Perimeter = 456 km

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6. Rectangle (2,000 m, 1,500 m)
Sides: 2000, 1500, 2000, 1500
Add: 2000 + 1500 = 3500 → 3500 + 2000 = 5500 → 5500 + 1500 = 7000 m

✔ Perimeter = 7000 m

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7. Hexagon (All sides same length: 178 m)
6 sides → 178 × 6
Calculate: 178 × 6
100×6=600, 70×6=420, 8×6=48 → 600+420=1020 → 1020+48= 1068 m

✔ Perimeter = 1068 m

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8. Square / Diamond (47 cm)
All 4 sides equal → 47 × 4 = 188 cm

✔ Perimeter = 188 cm

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9. Parallelogram (596 km, 677 km)
Opposite sides equal → so sides: 596, 677, 596, 677
Add: 596 + 677 = 1273 → 1273 + 596 = 1869 → 1869 + 677 = 2546 km

Check: 596×2 = 1192; 677×2 = 1354; 1192 + 1354 = 2546 ✔

✔ Perimeter = 2546 km

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Bonus Box: Which five shapes are quadrilaterals?

Quadrilateral = polygon with exactly 4 sides.

Look at each shape:

1. Rectangle → 4 sides → ✔
2. Trapezoid → 4 sides → ✔
3. Square → 4 sides → ✔
4. Isosceles Triangle → 3 sides → ✘
5. Octagon → 8 sides → ✘
6. Rectangle → 4 sides → ✔
7. Hexagon → 6 sides → ✘
8. Square/Diamond → 4 sides → ✔
9. Parallelogram → 4 sides → ✔

So quadrilaterals are:
→ Rectangle (first), Trapezoid, Square (small), Rectangle (big), Square/Diamond, Parallelogram → That’s 6? Wait, let’s count again.

List:

1. Rectangle → quad
2. Trapezoid → quad
3. Square → quad
4. Triangle → not
5. Octagon → not
6. Rectangle → quad
7. Hexagon → not
8. Square/Diamond → quad
9. Parallelogram → quad

That’s 6 quadrilaterals? But bonus says “five of the shapes above are quadrilaterals”. Hmm.

Wait — maybe they consider “Square” and “Square/Diamond” as same type? Or perhaps miscount?

Actually, let’s list the shapes as numbered in order:

Shape 1: Rectangle → quad
Shape 2: Trapezoid → quad
Shape 3: Square → quad
Shape 4: Triangle → no
Shape 5: Octagon → no
Shape 6: Rectangle → quad
Shape 7: Hexagon → no
Shape 8: Square/Diamond → quad
Shape 9: Parallelogram → quad

That’s 6 quads. But bonus says “five”. Maybe they don’t count the second rectangle? Or perhaps the diamond is considered same as square? But still 6.

Wait — perhaps the “Square” (shape 3) and “Square/Diamond” (shape 8) are both squares, but still two separate shapes.

Maybe the problem considers “quadrilaterals” as distinct types? But no, it says “shapes above”, meaning the 9 figures.

Perhaps I made a mistake — let’s recount the shapes shown:

From top row:
- Rectangle (1)
- Trapezoid (2)
- Square (3)

Middle row:
- Triangle (4)
- Octagon (5)
- Rectangle (6)

Bottom row:
- Hexagon (7)
- Square/Diamond (8)
- Parallelogram (9)

Yes, 9 shapes.

Quadrilaterals: 1,2,3,6,8,9 → six.

But bonus says “five”. Perhaps the “Square” and “Square/Diamond” are considered the same category? But the instruction is to shade the five quadrilaterals — meaning five of the nine drawings.

Wait — maybe the octagon is not counted correctly? Or perhaps the parallelogram is not considered? No.

Another thought: maybe the “Rectangle” in middle row is same as first? Still two separate shapes.

Perhaps the problem has a typo? Or maybe I should go with what’s obvious.

Standard definition: any 4-sided polygon is quadrilateral.

So shapes 1,2,3,6,8,9 are quadrilaterals → 6.

But since bonus says “five”, perhaps they exclude one? Maybe the diamond is not considered a different shape? Unlikely.

Wait — look back at the image description: the “Square/Diamond” is labeled as “Square / Diamond” — perhaps they consider it as one type, but still it’s a shape.

Alternatively, maybe the trapezoid is not considered? No.

Perhaps the answer expects us to pick five, and there are actually five if we miscount.

Let me list again carefully:

1. Rectangle — 4 sides — quad
2. Trapezoid — 4 sides — quad
3. Square — 4 sides — quad
4. Triangle — 3 — no
5. Octagon — 8 — no
6. Rectangle — 4 — quad
7. Hexagon — 6 — no
8. Rhombus (diamond) — 4 — quad
9. Parallelogram — 4 — quad

Still 6.

Unless... the "Square" and "Square/Diamond" are the same shape visually? But in the worksheet, they are separate boxes.

Perhaps the bonus is tricking us — but I think for accuracy, there are six quadrilaterals. However, since the problem says "five", maybe they don't count the second rectangle? Or perhaps in some curricula, rhombus is not called quadrilateral? No, that's wrong.

Another idea: perhaps the "Octagon (Symmetrical)" is drawn with 4 sides visible but actually has 8, which we already did.

I think there might be an error in the problem, but for student purposes, we'll identify the clear quadrilaterals.

The five most obvious ones might be: Rectangle, Trapezoid, Square, Rectangle (second), Parallelogram — leaving out the diamond? But diamond is also quadrilateral.

Perhaps the "Square/Diamond" is intended to be the same as square, but still.

To resolve: let's see common practice. In many worksheets, they include all 4-sided figures.

But since the bonus says "five", and there are nine shapes, likely they expect:

- First rectangle
- Trapezoid
- Small square
- Second rectangle
- Parallelogram

And omit the diamond? But that doesn't make sense.

Wait — shape 8 is labeled "Square / Diamond" — perhaps it's meant to be a rhombus, and they consider it under square, but still a separate shape.

I think for correctness, I'll state that there are six quadrilaterals, but since the problem says five, perhaps it's a mistake. For the student, we can say the quadrilaterals are the ones with four sides: shapes 1,2,3,6,8,9.

But to match the bonus, maybe they want us to choose five, so perhaps exclude the diamond or something.

Another thought: in the octagon, if it's symmetrical and we assumed 8 sides, but maybe it's not? No, we calculated based on labels.

Perhaps the "Isosceles Triangle" is misread, but no.

I recall that sometimes "quadrilateral" excludes self-intersecting, but all here are simple.

I think for the purpose of this exercise, we'll list the five that are unambiguously quadrilaterals and commonly recognized: Rectangle, Trapezoid, Square, Rectangle (again), Parallelogram — and perhaps the diamond is extra.

But let's check online or standard: all 4-sided polygons are quadrilaterals.

Perhaps the answer is to shade: 1,2,3,6,9 — omitting 8? Why?

Shape 8 is "Square / Diamond" — if it's a square rotated, it's still a quadrilateral.

I think there's a discrepancy, but for the student, we can say:

The quadrilaterals are: the two rectangles, the trapezoid, the small square, the parallelogram, and the diamond — that's six. But since the bonus says five, perhaps the diamond is not to be shaded? Unlikely.

Maybe "Square" and "Square/Diamond" are considered the same, but they are separate items.

I will proceed with the calculation part, and for bonus, list the five as per common expectation.

Upon second thought, let's count the shapes as presented in rows:

Row 1: 3 shapes — all quadrilaterals except none, all are 4-sided? Rectangle, trapezoid, square — all quad.

Row 2: triangle (not), octagon (not), rectangle (quad) — so one quad.

Row 3: hexagon (not), square/diamond (quad), parallelogram (quad) — two quads.

Total: row1:3, row2:1, row3:2 → 6.

Perhaps the octagon is not 8-sided? But it's labeled octagon.

I think for the sake of completing, I'll provide the perimeters, and for bonus, say the quadrilaterals are shapes 1,2,3,6,8,9 — but since it says five, maybe it's a typo, and we can box the answer as per calculation.

For the final answer, we need to output the perimeters and the bonus.

But the user didn't ask for bonus in the response format, only the perimeters are to be filled.

Looking back at the user's request: "Solve the problem accurately." and the problem is to find perimeter of each polygon.

The bonus is additional, but not required for the main answer.

In the response, we should provide the perimeters for the 9 shapes.

So let's compile:

1. Rectangle: 210 km
2. Trapezoid: 129 cm
3. Square: 92 m
4. Isosceles Triangle: 701 cm
5. Octagon: 456 km
6. Rectangle: 7000 m
7. Hexagon: 1068 m
8. Square/Diamond: 188 cm
9. Parallelogram: 2546 km

For bonus, if needed, but since the options are false, we don't explain.

Final Answer should be the perimeters listed.

But how to present? Probably as a list.

Since the worksheet has blanks, we can fill them.

For the response, we'll write the perimeters in order.

Also, verify calculations once more.

1. 38+67+38+67: 38*2=76, 67*2=134, 76+134=210 ✓
2. 67+22+18+22: 67+18=85, 22+22=44, 85+44=129 ✓
3. 23*4=92 ✓
4. 249+249+203: 249*2=498, 498+203=701 ✓
5. As above: 134*2=268, 23*4=92, 48*2=96, 268+92=360, 360+96=456 ✓
6. 2000*2=4000, 1500*2=3000, 4000+3000=7000 ✓
7. 178*6: 170*6=1020, 8*6=48, 1020+48=1068 ✓
8. 47*4=188 ✓
9. 596*2=1192, 677*2=1354, 1192+1354=2546 ✓

All correct.

For bonus, although not required, if we must, the five quadrilaterals could be interpreted as: the two rectangles, trapezoid, square, and parallelogram — omitting the diamond, but that's arbitrary. Perhaps in some contexts, diamond is not distinguished, but I think it's fine.

Since the user options are false, we don't need to address bonus in explanation.

So Final Answer is the list of perimeters.

We'll present them in order as per the worksheet.

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Final Answer:
Perimeter of Rectangle (38 km, 67 km): 210 km
Perimeter of Trapezoid (67 cm, 22 cm, 18 cm, 22 cm): 129 cm
Perimeter of Square (23 m): 92 m
Perimeter of Isosceles Triangle (249 cm, 249 cm, 203 cm): 701 cm
Perimeter of Octagon (Symmetrical): 456 km
Perimeter of Rectangle (2,000 m, 1,500 m): 7,000 m
Perimeter of Hexagon (178 m each side): 1,068 m
Perimeter of Square / Diamond (47 cm): 188 cm
Perimeter of Parallelogram (596 km, 677 km): 2,546 km