Certainly! Let's break down the problem step-by-step:
1. Calculate the area of the square ground:
- Side length of the square ground = 10 meters
- Area of the square ground = side × side = [tex]\(10 \, \text{m} \times 10 \, \text{m} = 100 \, \text{m}^2\)[/tex]
2. Determine the dimensions of the total area including the paved path:
- The width of the rectangular path on one side is 2 meters.
- Since the path is paved around all four sides of the square, an additional 2 meters will be added to each side of the square on both the length and the width.
- Thus, the total length will be:
[tex]\( \text{Side of square} + 2(\text{Width of path}) = 10 \, \text{m} + 2 \times 2 \, \text{m} = 14 \, \text{m} \)[/tex]
- Similarly, the total width will be:
[tex]\( \text{Side of square} + 2(\text{Width of path}) = 10 \, \text{m} + 2 \times 2 \, \text{m} = 14 \, \text{m} \)[/tex]
3. Calculate the total area including the paved path:
- The total area will be [tex]\( \text{Total length} \times \text{Total width} = 14 \, \text{m} \times 14 \, \text{m} = 196 \, \text{m}^2 \)[/tex]
4. Calculate the area of the rectangular paved path:
- The area of the paved path is the total area including the path minus the area of the square ground.
- Area of the rectangular paved path = [tex]\( 196 \, \text{m}^2 - 100 \, \text{m}^2 = 96 \, \text{m}^2 \)[/tex]
So, the total area of the rectangular paved path is [tex]\( 96 \, \text{m}^2 \)[/tex].
