Arrange 9 square tiles having side of lengths2cm in different ways. Find the perimeter of The resulting figure in each case.
so, did you do it?
To find the perimeter of different figures formed by arranging square tiles, we need to consider the arrangement of the tiles and count the total length of the outer boundary of the figure. The perimeter is the sum of the lengths of all the sides.
Let's consider the different ways to arrange the 9 square tiles with sides of length 2cm:
1. Square arrangement (3x3):
In this arrangement, the 9 tiles form a larger square.
The perimeter of a square is calculated by multiplying the length of one side by 4.
Perimeter = 2cm x 4 = 8cm
2. Rectangle arrangement (3x3):
In this arrangement, the 9 tiles form a rectangle.
The perimeter of a rectangle is calculated by adding the lengths of two adjacent sides and then multiplying by 2.
Perimeter = (2cm + 2cm) x 2 = 8cm
3. L-shape arrangement:
In this arrangement, 8 square tiles are arranged in the form of an L-shape, leaving one tile separate.
The perimeter of the L-shape arrangement depends on the orientation of the L-shape.
Let's consider the shorter side of the L-shape as the base, which is 4cm in length.
Perimeter = (4cm + 4cm) + (2cm + 2cm) = 12cm
4. Zigzag arrangement:
In this arrangement, the 9 tiles are arranged in a zigzag pattern with alternate tiles overlapping partially.
The perimeter of the zigzag arrangement will depend on the actual arrangement and pattern.
Let's assume that the complete length of the zigzag is 8cm.
Perimeter = 8cm + 2cm = 10cm
Note: The actual perimeter of the zigzag arrangement may differ based on how the tiles are overlapped.
So, the perimeters of the resulting figures in each case are as follows:
1. Square arrangement: 8cm
2. Rectangle arrangement: 8cm
3. L-shape arrangement: 12cm
4. Zigzag arrangement: 10cm