Semicircle — If the area of a semicircle is 77 sq m, find its perimeter (use perimeter = πr + 2r for a semicircle).

Introduction / Context:This problem tests formulas for a circle and a semicircle. For a semicircle of radius r, the area is (1/2) * π * r^2 and the perimeter (often called the boundary length) equals πr + 2r because it includes the curved arc (half the circumference) plus the diameter as the straight edge.

Given Data / Assumptions:

• Area of semicircle = 77 sq m
• Use π ≈ 22/7 for exact nice arithmetic
• Perimeter of semicircle P = πr + 2r

Concept / Approach:First recover the radius from the given area. Then plug r into the perimeter expression πr + 2r. With π = 22/7 here, the arithmetic becomes exact.

Step-by-Step Solution:(1/2) * π * r^2 = 77(1/2) * (22/7) * r^2 = 77 ⇒ r^2 = 154 / (22/7) = 49 ⇒ r = 7 mPerimeter P = πr + 2r = (22/7)*7 + 14 = 22 + 14 = 36 m

Verification / Alternative check:Back-substitute r = 7 in area formula for a semicircle to reconfirm 77 sq m, which matches the prompt exactly.

Why Other Options Are Wrong:42 m, 48 m, and 54 m arise from misusing full circumference or omitting the diameter term; 32 m comes from mixing up half/whole factors.

Common Pitfalls:Using full-circle perimeter 2πr or forgetting to add the diameter when computing the boundary length of a semicircle.

Final Answer:36 m