The area (in m²) of a circular path of uniform width x metres surrounding a circular region of diameter d metres is _____.

$πx(x + d)$

We know that,

Area of path = π(R² – r²)

According to the question,

Radius of circular region (r) = d/2

Width of path = x m

External radius of path (R) = d/2 + x

We know that,

Area of path = π(R² – r²) = π[(d/2 + x)² – (d/2)²] = π [d²/4 + x² + dx – d²/4] = π [x² + dx]

= πx (x + d)