Perimeter worksheet for students to calculate and compare the perimeter of two shapes on a grid.

To find the perimeter of a shape on a grid, we count the number of unit lengths along the outside edge. Since each square side is 1 cm, the number of sides equals the perimeter in centimeters.

Here is the step-by-step calculation for each pair:

a)
* Shape A: Let's trace the outside edges.
* Top: 3 segments
* Right side (upper part): 2 segments down
* Inner horizontal: 2 segments left
* Inner vertical: 1 segment down
* Bottom right vertical: 1 segment down
* Bottom: 5 segments left
* Left side: 4 segments up
* Total: $3 + 2 + 2 + 1 + 1 + 5 + 4 = 18$ cm.
* Shape B: Let's trace the outside edges.
* Top: 2 segments
* Right upper vertical: 2 segments down
* Middle horizontal: 2 segments right
* Lower right vertical: 2 segments down
* Bottom: 4 segments left
* Left side: 4 segments up
* Total: $2 + 2 + 2 + 2 + 4 + 4 = 16$ cm.

b)
* Shape A:
* Top: 3 segments
* Right upper vertical: 1 segment down
* Inner horizontal: 1 segment left
* Inner vertical: 1 segment down
* Bottom right vertical: 1 segment down
* Bottom: 4 segments left
* Left side: 3 segments up
* Total: $3 + 1 + 1 + 1 + 1 + 4 + 3 = 14$ cm.
* Shape B:
* Top: 3 segments
* Right upper vertical: 1 segment down
* Inner horizontal: 1 segment left
* Inner vertical: 2 segments down
* Bottom: 4 segments left
* Left side: 3 segments up
* Total: $3 + 1 + 1 + 2 + 4 + 3 = 14$ cm.

c)
* Shape A:
* Top: 4 segments
* Right upper vertical: 1 segment down
* Inner horizontal: 2 segments left
* Inner vertical: 1 segment down
* Inner horizontal: 2 segments left
* Inner vertical: 1 segment down
* Bottom: 4 segments left
* Left side: 3 segments up
* Total: $4 + 1 + 2 + 1 + 2 + 1 + 4 + 3 = 18$ cm.
* Shape B: This is a cross shape.
* It has 12 outer edges (each "arm" of the cross contributes 3 sides, but they share corners, so let's just count around).
* Starting from top-left of the top arm and going clockwise: 1 right, 1 down, 1 right, 1 down, 1 left, 1 down, 1 left, 1 up, 1 left, 1 up, 1 right, 1 up.
* Total: 12 cm.

d)
* Shape A:
* Top: 3 segments
* Right upper vertical: 2 segments down
* Inner horizontal: 2 segments left
* Inner vertical: 1 segment down
* Inner horizontal: 2 segments right
* Lower right vertical: 1 segment down
* Bottom: 5 segments left
* Left side: 4 segments up
* Total: $3 + 2 + 2 + 1 + 2 + 1 + 5 + 4 = 20$ cm.
* Shape B: This is a symmetric cross-like shape.
* Top: 1 segment
* Top-right vertical: 1 segment down
* Right-upper horizontal: 1 segment right
* Right-middle vertical: 1 segment down
* Right-lower horizontal: 1 segment left
* Bottom-right vertical: 1 segment down
* Bottom: 1 segment left
* Bottom-left vertical: 1 segment up
* Left-lower horizontal: 1 segment left
* Left-middle vertical: 1 segment up
* Left-upper horizontal: 1 segment right
* Top-left vertical: 1 segment up
* Total: 12 cm.

Final Answer:
a) Perimeter of shape A = 18 cm
Perimeter of shape B = 16 cm

b) Perimeter of shape A = 14 cm
Perimeter of shape B = 14 cm

c) Perimeter of shape A = 18 cm
Perimeter of shape B = 12 cm

d) Perimeter of shape A = 20 cm
Perimeter of shape B = 12 cm