Perimeter Shape Problems Worksheet - Free Printable
Educational worksheet: Perimeter Shape Problems Worksheet. Download and print for classroom or home learning activities.
JPG
773×1000
50.8 KB
Free · Personal Use
Quality Assured by Worksheets Library Team
Reviewed for educational accuracy and age-appropriateness
ID: #1625134
⭐
Show Answer Key & Explanations
Step-by-step solution for: Perimeter Shape Problems Worksheet
▼
Show Answer Key & Explanations
Step-by-step solution for: Perimeter Shape Problems Worksheet
Let’s solve each perimeter problem one by one. Remember: Perimeter = add up all the sides of the shape.
---
1. Square with side 23 mm
All 4 sides are equal in a square.
So, 23 + 23 + 23 + 23 = 92 mm
Or: 4 × 23 = 92 mm
✔ Perimeter = 92 mm
---
2. Pentagon with sides: 14 in, 12 in, 13 in, 14 in, 11 in
Add them all:
14 + 12 = 26
26 + 13 = 39
39 + 14 = 53
53 + 11 = 64
✔ Perimeter = 64 in
---
3. Triangle with base 27 ft — but wait! Only one side is given?
Looking again — it’s an equilateral triangle? No label says that. But in many worksheets like this, if only one side is shown and it looks symmetric, they might mean all sides are equal. However, let’s check the image description — actually, in the original problem, only the bottom side is labeled “27 ft”. That can’t be right for perimeter unless we assume it’s equilateral.
Wait — looking back at the user’s image description (even though I’m not describing it), in standard problems like this, if only one side is given on a triangle and no other info, it’s often meant to be equilateral. Let me double-check logic.
Actually — re-examining common worksheet patterns: Problem #3 shows a triangle with only the base labeled 27 ft. But since it’s drawn as equilateral (all sides look same), and no other labels, we’ll assume all three sides are 27 ft.
So: 27 + 27 + 27 = 81 ft
Or 3 × 27 = 81 ft
✔ Perimeter = 81 ft
*(Note: If this were not equilateral, we’d need more info — but based on typical grade-level problems, this assumption is safe.)*
---
4. Rectangle: length 145 m, width 72 m
Rectangle has two lengths and two widths.
So: 145 + 145 + 72 + 72
= (145 × 2) + (72 × 2)
= 290 + 144 = 434 m
✔ Perimeter = 434 m
---
5. Irregular pentagon: sides 35 cm, 31 cm, 46 cm, 26 cm, 13 cm, 30 cm — wait, that’s 6 sides?
Let’s list them from the image description:
Top: 35 cm
Right top: 31 cm
Right bottom: 46 cm
Bottom: 26 cm
Left bottom: 13 cm
Left top: 30 cm → yes, 6 sides? Wait, that would be a hexagon.
Wait — counting again:
From the labels: 35, 31, 46, 26, 13, 30 → six numbers → so it’s a hexagon? But called "pentagon" in my head? No — just add whatever sides are given.
Add:
35 + 31 = 66
66 + 46 = 112
112 + 26 = 138
138 + 13 = 151
151 + 30 = 181
✔ Perimeter = 181 cm
---
6. Triangle: sides 95 yds, 206 yds, 246 yds
Add:
95 + 206 = 301
301 + 246 = 547
✔ Perimeter = 547 yds
---
7. Diamond (rhombus) with one side 3.5 km
All sides equal in rhombus. So 4 sides × 3.5 km
3.5 × 4 = 14 km
✔ Perimeter = 14 km
---
8. Irregular quadrilateral? Sides: 56 mi, 45 mi, 45 mi, 63 mi, 82 mi — wait, that’s 5 sides?
List: left side 56 mi, top-left slant 45 mi, top-right slant 45 mi, right side 63 mi, bottom 82 mi → yes, 5 sides → pentagon.
Add:
56 + 45 = 101
101 + 45 = 146
146 + 63 = 209
209 + 82 = 291
✔ Perimeter = 291 mi
---
9. Arrow-shaped figure: sides 1,200 mm, 400 mm, 750 mm, and then...?
This is tricky. The arrow has:
- Long horizontal top: 1,200 mm
- Vertical down on right: 400 mm
- Diagonal tip: 750 mm
But what about the rest? In such shapes, usually the bottom mirrors the top, and the left side is straight.
Actually, looking at standard arrow perimeters:
It typically has:
Top: 1200 mm
Right vertical: 400 mm
Diagonal right: 750 mm
Then diagonal left (same as right?): also 750 mm?
Then left vertical: same as right? 400 mm?
And bottom: same as top? 1200 mm?
Wait — that would make it symmetric. Let’s assume symmetry because otherwise we don’t have enough data.
So sides:
Top: 1200
Right-down: 400
Tip-right: 750
Tip-left: 750 (mirror)
Left-up: 400 (mirror)
Bottom: 1200 (mirror)
But that’s 6 sides. Add:
1200 + 400 = 1600
1600 + 750 = 2350
2350 + 750 = 3100
3100 + 400 = 3500
3500 + 1200 = 4700
Wait — but maybe the bottom isn't full length? Actually, in many such diagrams, the arrowhead replaces part of the rectangle.
Alternative approach: Think of it as a rectangle plus a triangle on the end.
But simpler: Since only three sides are labeled (1200, 400, 750), and it's symmetric, the total perimeter should include:
- Two long horizontals: 1200 each → 2400
- Two short verticals: 400 each → 800
- Two diagonals: 750 each → 1500
Total: 2400 + 800 = 3200; 3200 + 1500 = 4700 mm
✔ Perimeter = 4,700 mm
*(Note: This assumes symmetry, which is standard for such textbook figures when not fully labeled.)*
---
10. Rectangle: height 140 in, width 66 in
Two heights, two widths:
140 + 140 + 66 + 66
= 280 + 132 = 412 in
✔ Perimeter = 412 in
---
Now, compiling all answers:
1. 92 mm
2. 64 in
3. 81 ft
4. 434 m
5. 181 cm
6. 547 yds
7. 14 km
8. 291 mi
9. 4,700 mm
10. 412 in
Final Answer:
1. 92 mm
2. 64 in
3. 81 ft
4. 434 m
5. 181 cm
6. 547 yds
7. 14 km
8. 291 mi
9. 4700 mm
10. 412 in
---
1. Square with side 23 mm
All 4 sides are equal in a square.
So, 23 + 23 + 23 + 23 = 92 mm
Or: 4 × 23 = 92 mm
✔ Perimeter = 92 mm
---
2. Pentagon with sides: 14 in, 12 in, 13 in, 14 in, 11 in
Add them all:
14 + 12 = 26
26 + 13 = 39
39 + 14 = 53
53 + 11 = 64
✔ Perimeter = 64 in
---
3. Triangle with base 27 ft — but wait! Only one side is given?
Looking again — it’s an equilateral triangle? No label says that. But in many worksheets like this, if only one side is shown and it looks symmetric, they might mean all sides are equal. However, let’s check the image description — actually, in the original problem, only the bottom side is labeled “27 ft”. That can’t be right for perimeter unless we assume it’s equilateral.
Wait — looking back at the user’s image description (even though I’m not describing it), in standard problems like this, if only one side is given on a triangle and no other info, it’s often meant to be equilateral. Let me double-check logic.
Actually — re-examining common worksheet patterns: Problem #3 shows a triangle with only the base labeled 27 ft. But since it’s drawn as equilateral (all sides look same), and no other labels, we’ll assume all three sides are 27 ft.
So: 27 + 27 + 27 = 81 ft
Or 3 × 27 = 81 ft
✔ Perimeter = 81 ft
*(Note: If this were not equilateral, we’d need more info — but based on typical grade-level problems, this assumption is safe.)*
---
4. Rectangle: length 145 m, width 72 m
Rectangle has two lengths and two widths.
So: 145 + 145 + 72 + 72
= (145 × 2) + (72 × 2)
= 290 + 144 = 434 m
✔ Perimeter = 434 m
---
5. Irregular pentagon: sides 35 cm, 31 cm, 46 cm, 26 cm, 13 cm, 30 cm — wait, that’s 6 sides?
Let’s list them from the image description:
Top: 35 cm
Right top: 31 cm
Right bottom: 46 cm
Bottom: 26 cm
Left bottom: 13 cm
Left top: 30 cm → yes, 6 sides? Wait, that would be a hexagon.
Wait — counting again:
From the labels: 35, 31, 46, 26, 13, 30 → six numbers → so it’s a hexagon? But called "pentagon" in my head? No — just add whatever sides are given.
Add:
35 + 31 = 66
66 + 46 = 112
112 + 26 = 138
138 + 13 = 151
151 + 30 = 181
✔ Perimeter = 181 cm
---
6. Triangle: sides 95 yds, 206 yds, 246 yds
Add:
95 + 206 = 301
301 + 246 = 547
✔ Perimeter = 547 yds
---
7. Diamond (rhombus) with one side 3.5 km
All sides equal in rhombus. So 4 sides × 3.5 km
3.5 × 4 = 14 km
✔ Perimeter = 14 km
---
8. Irregular quadrilateral? Sides: 56 mi, 45 mi, 45 mi, 63 mi, 82 mi — wait, that’s 5 sides?
List: left side 56 mi, top-left slant 45 mi, top-right slant 45 mi, right side 63 mi, bottom 82 mi → yes, 5 sides → pentagon.
Add:
56 + 45 = 101
101 + 45 = 146
146 + 63 = 209
209 + 82 = 291
✔ Perimeter = 291 mi
---
9. Arrow-shaped figure: sides 1,200 mm, 400 mm, 750 mm, and then...?
This is tricky. The arrow has:
- Long horizontal top: 1,200 mm
- Vertical down on right: 400 mm
- Diagonal tip: 750 mm
But what about the rest? In such shapes, usually the bottom mirrors the top, and the left side is straight.
Actually, looking at standard arrow perimeters:
It typically has:
Top: 1200 mm
Right vertical: 400 mm
Diagonal right: 750 mm
Then diagonal left (same as right?): also 750 mm?
Then left vertical: same as right? 400 mm?
And bottom: same as top? 1200 mm?
Wait — that would make it symmetric. Let’s assume symmetry because otherwise we don’t have enough data.
So sides:
Top: 1200
Right-down: 400
Tip-right: 750
Tip-left: 750 (mirror)
Left-up: 400 (mirror)
Bottom: 1200 (mirror)
But that’s 6 sides. Add:
1200 + 400 = 1600
1600 + 750 = 2350
2350 + 750 = 3100
3100 + 400 = 3500
3500 + 1200 = 4700
Wait — but maybe the bottom isn't full length? Actually, in many such diagrams, the arrowhead replaces part of the rectangle.
Alternative approach: Think of it as a rectangle plus a triangle on the end.
But simpler: Since only three sides are labeled (1200, 400, 750), and it's symmetric, the total perimeter should include:
- Two long horizontals: 1200 each → 2400
- Two short verticals: 400 each → 800
- Two diagonals: 750 each → 1500
Total: 2400 + 800 = 3200; 3200 + 1500 = 4700 mm
✔ Perimeter = 4,700 mm
*(Note: This assumes symmetry, which is standard for such textbook figures when not fully labeled.)*
---
10. Rectangle: height 140 in, width 66 in
Two heights, two widths:
140 + 140 + 66 + 66
= 280 + 132 = 412 in
✔ Perimeter = 412 in
---
Now, compiling all answers:
1. 92 mm
2. 64 in
3. 81 ft
4. 434 m
5. 181 cm
6. 547 yds
7. 14 km
8. 291 mi
9. 4,700 mm
10. 412 in
Final Answer:
1. 92 mm
2. 64 in
3. 81 ft
4. 434 m
5. 181 cm
6. 547 yds
7. 14 km
8. 291 mi
9. 4700 mm
10. 412 in
Parent Tip: Review the logic above to help your child master the concept of perimeter problems worksheet.
