Sector area from radius and central angle: Find the area of a sector of a circle with radius 12 m and central angle 42°.

Introduction / Context:Sector area scales with the fraction of the full angle: (θ/360) of the full circle’s area. Plug the radius and given angle directly.

Given Data / Assumptions:

• r = 12 m
• θ = 42°
• Area(circle) = πr^2

Concept / Approach:A_sector = (θ/360) * π * r^2. Compute numerically without rounding too early.

Step-by-Step Solution:A_sector = (42/360) * π * 12^2 = (7/60) * π * 144= (1008/60) * π = 16.8π ≈ 52.8 sq. meters

Verification / Alternative check:Using π = 22/7: 16.8 * 22/7 = 52.8 exactly, matching the option.

Why Other Options Are Wrong:26.4 and 39.6 undercount; 79.2 overcounts; 63.0 does not correspond to this angle fraction.

Common Pitfalls:Using degrees directly as radians; forgetting to square the radius; mixing up 42 with 72 in mental math.

Final Answer:52.8 sq. meters