Perimeter of L Shapes Worksheets - Free Printable

To find the perimeter of an L-shape, we need to add up the lengths of all the outer sides. A helpful trick for L-shapes is that the sum of the horizontal segments on one side equals the total width, and the sum of the vertical segments on one side equals the total height. This means the perimeter is often equal to $(2 \times \text{Total Width}) + (2 \times \text{Total Height})$, just like a rectangle. However, we must be careful to identify which numbers represent the full length/width and which are partial segments.

Let's solve each problem step-by-step.

Problem 1:
- Vertical sides: The left side is $11$ in. The right side has two parts: $5$ in and the bottom part. Wait, looking at the shape, the left side is the total height ($11$ in). The top horizontal part is $3$ in. The inner vertical drop is $5$ in. The bottom horizontal part is $9$ in.
- Let's trace the perimeter:
- Left side: $11$ in
- Top side: $3$ in
- Inner vertical side: $5$ in
- Inner horizontal side: We need to calculate this. The total width at the bottom is $9$ in. The top width is $3$ in. So the inner horizontal segment is $9 - 3 = 6$ in? No, looking at the diagram, the $9$ in is the bottom width. The top part sticks out $3$ in. The vertical part going down is $5$ in. The left side is $11$ in.
- Let's look at the labels again.
- Left vertical: $11$ in
- Top horizontal: $3$ in
- Inner vertical: $5$ in
- Bottom horizontal: $9$ in
- We are missing the rightmost vertical side and the inner horizontal side connecting the $5$ in drop to the bottom.
- Actually, usually in these problems, the outer bounding box dimensions can be used.
- Total Height = $11$ in.
- Total Width = $9$ in.
- Perimeter = $2 \times (\text{Height} + \text{Width}) = 2 \times (11 + 9) = 2 \times 20 = 40$ in.
- Let's verify by adding individual sides.
- Left: $11$
- Top: $3$
- Right-top vertical: The label $5$ in is next to the inner vertical edge. So the inner vertical edge is $5$ in.
- The remaining vertical edge on the far right? No, the shape is an L.
- Let's trace clockwise from top-left:
1. Top: $3$ in
2. Down (inner): $5$ in
3. Right (inner horizontal): This length is Total Width ($9$) - Top Width ($3$) = $6$ in.
4. Down (rightmost): This length is Total Height ($11$) - Inner Vertical ($5$) = $6$ in.
5. Bottom: $9$ in
6. Left: $11$ in
- Sum: $3 + 5 + 6 + 6 + 9 + 11 = 40$ in.
- Answer: 40 in

Problem 2:
- Units: yards (yd)
- Total Height: The left side is $7$ yd.
- Total Width: The bottom side is $6$ yd.
- Using the rectangle rule: Perimeter = $2 \times (7 + 6) = 2 \times 13 = 26$ yd.
- Let's verify with given inner labels:
- Left: $7$
- Top: Unknown directly, but we have inner vertical $4$ yd and inner horizontal $3$ yd.
- Let's trace:
- Left: $7$
- Top: Total Width ($6$) - Inner Horizontal ($3$) = $3$ yd.
- Inner Vertical: $4$ yd.
- Inner Horizontal: $3$ yd.
- Right Vertical: Total Height ($7$) - Inner Vertical ($4$) = $3$ yd.
- Bottom: $6$ yd.
- Sum: $7 + 3 + 4 + 3 + 3 + 6 = 26$ yd.
- Answer: 26 yd

Problem 3:
- Units: inches (in)
- Total Height: Left side is $8$ in.
- Total Width: Bottom side is $10$ in.
- Perimeter = $2 \times (8 + 10) = 2 \times 18 = 36$ in.
- Check with inner labels: Top right horizontal is $3$ in. Inner vertical is $5$ in.
- Left: $8$
- Top: Total Width ($10$) - Top Right ($3$) = $7$ in.
- Inner Vertical: $5$ in.
- Inner Horizontal: $3$ in.
- Right Vertical: Total Height ($8$) - Inner Vertical ($5$) = $3$ in.
- Bottom: $10$ in.
- Sum: $8 + 7 + 5 + 3 + 3 + 10 = 36$ in.
- Answer: 36 in

Problem 4:
- Units: cm
- Total Height: Left side is $6$ cm.
- Total Width: Bottom side is $9$ cm.
- Perimeter = $2 \times (6 + 9) = 2 \times 15 = 30$ cm.
- Check labels: Top vertical drop is $2$ cm. Inner horizontal is $4$ cm.
- Left: $6$
- Top: Total Width ($9$) - Inner Horizontal ($4$) = $5$ cm.
- Inner Vertical: $2$ cm.
- Inner Horizontal: $4$ cm.
- Right Vertical: Total Height ($6$) - Inner Vertical ($2$) = $4$ cm.
- Bottom: $9$ cm.
- Sum: $6 + 5 + 2 + 4 + 4 + 9 = 30$ cm.
- Answer: 30 cm

Problem 5:
- Units: mm
- Total Height: Right side is $8$ mm.
- Total Width: Top side is $9$ mm.
- Perimeter = $2 \times (8 + 9) = 2 \times 17 = 34$ mm.
- Check labels: Inner vertical is $5$ mm. Inner horizontal is $2$ mm.
- Top: $9$
- Right: $8$
- Bottom: Total Width ($9$) - Inner Horizontal ($2$) = $7$ mm? No, let's look at the shape orientation.
- It's an inverted L or rotated.
- Left side total height? The left side consists of a top part and a bottom part. The label $5$ mm is the inner vertical. The label $2$ mm is the inner horizontal.
- Let's assume standard orientation where "up" is top.
- Top width: $9$ mm.
- Right height: $8$ mm.
- Inner corner: The cutout is at the bottom left? No, the lines suggest the main block is top-right.
- Let's trace perimeter:
- Top: $9$
- Right: $8$
- Bottom: The bottom-most segment. Its length is Total Width ($9$) minus the top-left extension? No.
- Let's use the bounding box method which is robust.
- Max Width = $9$ mm.
- Max Height = $8$ mm.
- Perimeter = $2 \times (9 + 8) = 34$ mm.
- Answer: 34 mm

Problem 6:
- Units: yd
- Total Height: Right side is $5$ yd.
- Total Width: Top side is $6$ yd.
- Perimeter = $2 \times (6 + 5) = 2 \times 11 = 22$ yd.
- Check labels: Inner vertical is $4$ yd. Inner horizontal is $3$ yd.
- Top: $6$
- Right: $5$
- Bottom: Total Width ($6$) - Inner Horizontal ($3$) = $3$ yd.
- Inner Vertical: $4$ yd? Wait. If Right is $5$ and Inner Vertical is $4$, then the left vertical part is $5 - 4 = 1$? Or is the $4$ yd the left part?
- Looking at the diagram: The left side has a vertical segment labeled $4$ yd? No, the $4$ yd is inside the corner. Usually, that indicates the length of the segment parallel to it.
- Let's assume the $4$ yd is the vertical segment of the "cutout" or the inner vertical wall. And $3$ yd is the inner horizontal wall.
- Total Height = $5$ yd. Total Width = $6$ yd.
- Perimeter = $22$ yd.
- Answer: 22 yd

Problem 7:
- Units: cm
- Total Height: Left side is composed of $3$ cm and another segment? No, the left side has a label $3$ cm at the bottom and $9$ cm at the top?
- Let's look closely at Problem 7.
- Top horizontal: $9$ cm.
- Right vertical: $11$ cm.
- Bottom horizontal: There is a segment labeled $3$ cm.
- Left vertical: There is a segment labeled $3$ cm.
- This looks like the labels are for specific segments, not totals.
- Let's deduce the totals.
- The shape is an L rotated.
- Top width = $9$ cm.
- Right height = $11$ cm.
- Therefore, Total Width = $9$ cm, Total Height = $11$ cm.
- Perimeter = $2 \times (9 + 11) = 2 \times 20 = 40$ cm.
- Let's verify if the inner labels contradict this.
- Inner horizontal segment: The bottom has a $3$ cm segment on the left. The total width is $9$. So the inner horizontal part (connecting the left leg to the right leg) would be... wait.
- Let's trace the boundary.
- Top: $9$ cm.
- Right: $11$ cm.
- Bottom: The right part of the bottom. Length = Total Width ($9$) - Left Leg Width. We don't have the left leg width explicitly, but we have a bottom-left segment labeled $3$ cm? No, the label $3$ cm is on the bottom horizontal segment of the left protrusion.
- Left: The bottom part of the left vertical side is $3$ cm.
- This implies the "cutout" is at the top right? No, it's a standard L.
- Let's assume the outer boundaries are defined by the longest spans.
- Span Up-Down: The right side is $11$ cm. Is that the total height? Yes, it spans the whole side.
- Span Left-Right: The top side is $9$ cm. Is that the total width? Yes, it spans the whole top.
- So, Perimeter = $2 \times (11 + 9) = 40$ cm.
- Answer: 40 cm

Problem 8:
- Units: in
- Top horizontal: $8$ in.
- Right vertical: $8$ in.
- Inner labels: $5$ in (vertical) and $5$ in (horizontal).
- Total Width = $8$ in.
- Total Height = $8$ in.
- Perimeter = $2 \times (8 + 8) = 32$ in.
- Answer: 32 in

Problem 9:
- Units: m
- Left vertical: $11$ m.
- Bottom horizontal: $8$ m.
- Inner labels: $4$ m (horizontal) and $3$ m (vertical).
- Total Height = $11$ m.
- Total Width = $8$ m.
- Perimeter = $2 \times (11 + 8) = 2 \times 19 = 38$ m.
- Answer: 38 m

Problem 10:
- Units: mm
- Top horizontal: $12$ mm.
- Right vertical: $9$ mm.
- Inner labels: $6$ mm (vertical) and $5$ mm (horizontal).
- Total Width = $12$ mm.
- Total Height = $9$ mm.
- Perimeter = $2 \times (12 + 9) = 2 \times 21 = 42$ mm.
- Answer: 42 mm

Final Answer:
1. 40 in
2. 26 yd
3. 36 in
4. 30 cm
5. 34 mm
6. 22 yd
7. 40 cm
8. 32 in
9. 38 m
10. 42 mm