Navneet buys 9 square paving slabs, each with a side of 1/2 m.
Shruti does not like his arrangement. She gets him to lay them out like a cross.

The perimeter of Shruti’s arrangement is ____ m.

Step-by-Step Explanation & Solution

Step 1: Find Total Area

Each slab is a square with side 1/2 m. Area of one slab: (1/2 m)² = 1/4 m².

Total area for 9 slabs: 9 × (1/4 m²) = 9/4 m^2.

Step 2: Understand the Cross Arrangement

A cross (plus-sign shape) has a central square with arms extending in four directions. A simple Greek cross uses 5 squares, but the problem specifies 9 slabs; thus the intended cross uses longer arms so that the total count is 9 squares while preserving the cross shape.

The natural way to reach 9 is to have a central square and extend each of the four arms by two additional squares along the same line, making each arm three squares long including the center line.

Step 3: Count the Squares in the Cross

Central square: 1. Each of the 4 arms contributes 2 additional squares beyond the center, so total squares: 1 + 4 × 2 = 9.

Each square has side 0.5 m, so each arm spans 3 squares or 3 × 0.5 = 1.5 m from end to end along that arm’s line.

Step 4: Perimeter Calculation

The perimeter is the total length around the outer boundary of the cross. For this 9‑square cross, the boundary consists of the four long outer segments (one per direction) plus the four short end segments at the extremities.

Long outer segments: 4 × 1.5 m = 6 m. Short end segments: 4 × 0.5 m = 2 m. Therefore, total perimeter: 6 m + 2 m = 8 m.

Final Answer: 8 m