Finding the Perimeter | Interactive Worksheet - Free Printable

To find the perimeter of a shape, you add up the lengths of all its sides. Let's solve each problem one by one.

1. Hexagon (Top Left)
* This shape has 6 sides.
* Each side is 6 meters long.
* Calculation: $6 + 6 + 6 + 6 + 6 + 6 = 36$
* Answer: 36 meters

2. Pentagon (Top Middle)
* This shape has 5 sides.
* The sides are: 4 in, 4 in, 6 in, 6 in, and 3 in.
* Calculation: $4 + 4 + 6 + 6 + 3 = 23$
* Answer: 23 inches

3. Cross Shape (Top Right)
* Let's count all the outer edges. There are 12 sides in total.
* Four sides are 5 cm long.
* Eight sides are 2 cm long.
* Calculation: $(4 \times 5) + (8 \times 2) = 20 + 16 = 36$
* Answer: 36 centimeters

4. Octagon (Middle Left)
* This shape has 8 sides.
* Each side is 3 inches long.
* Calculation: $8 \times 3 = 24$
* Answer: 24 inches

5. L-Shape (Middle Center)
* We need to add all the outer edges.
* Given sides: 10 yds, 7 yds, 5 yds, 4 yds, 3 yds, 9 yds.
* *Note: Even though some inner lines aren't labeled, the total vertical length on the left (9) matches the right side segments ($5+4=9$), and the total horizontal width on top (10) matches the bottom segments ($3+7=10$). We just sum the visible boundary labels provided or implied.*
* Let's trace the outside: Top (10) + Right-top (7) + Inner-horizontal (5) + Inner-vertical (4) + Bottom-right (3) + Left (9). Wait, looking closely at the diagram labels:
* Top: 10
* Right side upper part: 7
* Inner horizontal step: 5
* Inner vertical step: 4
* Bottom right part: 3
* Left side: 9
* Let's check if we missed any. The bottom-left horizontal part isn't explicitly labeled with a number, but since the total width is 10 and the right part is 3? No, the label "3 yds" is under the short bottom leg. The label "5 yds" is the inner horizontal. The label "10 yds" is the top. So the bottom-left horizontal segment would be $10 - 5 = 5$? Or is the "3 yds" the bottom left? Let's look at the alignment.
* Actually, usually in these problems, you just add every number shown on the perimeter line.
* Sides shown: 10, 7, 5, 4, 3, 9.
* Is there a missing side? The bottom-left horizontal segment. If the top is 10 and the inner horizontal is 5, the remaining bottom part is likely 5. But there is a label "3 yds". Let's assume the labels define the specific segments they are next to.
* Let's re-read the shape carefully.
* Top: 10
* Right Vertical: 7
* Inner Horizontal: 5
* Inner Vertical: 4
* Bottom Right Horizontal: 3
* Left Vertical: 9
* There is a missing label for the bottom-left horizontal segment. However, geometrically, the total width at the bottom must equal the top (10). The bottom consists of the "3 yd" segment and the unknown segment. So the unknown segment is $10 - 3 = 7$? No, the "5 yd" is the inner cutout.
* Let's try another interpretation. Often, opposite parallel sides in rectilinear shapes are equal.
* Total Height = Left Side (9). Right side parts are 7 and 4? No, 7 is the top right vertical. 4 is the inner vertical. $7+4=11$, which doesn't match 9. This suggests the drawing might not be perfectly to scale or I am misinterpreting which label belongs to which line.
* Let's look at the standard way these worksheets work. You simply add the numbers given on the boundary.
* Boundary numbers: 10, 7, 5, 4, 3, 9.
* Sum: $10 + 7 + 5 + 4 + 3 + 9 = 38$.
* Let's double check for a hidden side. The shape is an L. It has 6 sides. All 6 sides have numbers next to them.
* Top: 10. Right: 7. Inner Horizontal: 5. Inner Vertical: 4. Bottom Right: 3. Left: 9.
* Wait, does the "3 yds" refer to the bottom-most horizontal segment? And the "5 yds" the inner horizontal? If so, the total width is $3 + (\text{something})$. The top is 10. So the left part of the bottom would be $10 - 3 = 7$? But the inner horizontal is labeled 5. This geometry is conflicting.
* Let's look at the verticals. Left is 9. Right is 7. Inner vertical is 4. $7+4=11$. This doesn't match 9.
* Let's reconsider the labels. Maybe the "5 yds" is the bottom horizontal part and "3 yds" is something else? No, the lines point clearly.
* Let's assume the question simply wants the sum of the labeled sides, as is common in lower-grade worksheets where geometry might be slightly imperfectly drawn.
* Sum: $10 + 7 + 5 + 4 + 3 + 9 = 38$.
* Alternative Check: If we assume it's a perfect rectangle with a chunk taken out, Perimeter = $2 \times (\text{Width} + \text{Height})$. Width=10, Height=9. Perimeter = $2 \times (10+9) = 38$. This works perfectly! In rectilinear shapes like this (where corners are right angles), the perimeter is often the same as the bounding box. The indented parts push out to equal the straight sides.
* So, Perimeter = $2 \times (10 + 9) = 38$.
* Answer: 38 yards

6. Trapezoid (Middle Right)
* This shape has 4 sides.
* The sides are: 9 ft, 7 ft, 5 ft, and 4 ft.
* Calculation: $9 + 7 + 5 + 4 = 25$
* Answer: 25 feet

7. Large L-Shape (Bottom Left)
* This is a rectilinear shape (all right angles).
* We can use the "bounding box" trick again. The total height is the longest vertical side (8 yds). The total width is the longest horizontal side (9 yds).
* Perimeter = $2 \times (\text{Height} + \text{Width})$
* Calculation: $2 \times (8 + 9) = 2 \times 17 = 34$
* Let's verify by adding sides individually to be sure.
* Left: 8
* Top: 6
* Inner Vertical: The total height is 8. The rightmost vertical is 3. So the inner vertical drop is $8 - 3 = 5$. (Label says 5 yds, matches).
* Inner Horizontal: The total width is 9. The top is 6. So the inner horizontal step is $9 - 6 = 3$. (Label says 3 yds, matches).
* Rightmost Vertical: 3
* Bottom: 9
* Sum: $8 + 6 + 5 + 3 + 3 + 9 = 34$.
* Answer: 34 yards

8. Hexagon (Bottom Middle)
* This shape has 6 sides.
* Each side is 8 meters long.
* Calculation: $6 \times 8 = 48$
* Answer: 48 meters

9. Pentagon (Bottom Right)
* This shape has 5 sides.
* The sides are: 4 ft, 5 ft, 5 ft, 5 ft, and 4 ft.
* Calculation: $4 + 5 + 5 + 5 + 4 = 23$
* Answer: 23 feet

Final Answer:
1. 36 meters
2. 23 inches
3. 36 centimeters
4. 24 inches
5. 38 yards
6. 25 feet
7. 34 yards
8. 48 meters
9. 23 feet