A semicircular window has diameter 63 cm. Find its perimeter (the curved edge plus the straight diameter).

Introduction / Context:Perimeter of a semicircle consists of the semicircular arc plus the straight diameter edge. Recognizing this avoids the common mistake of using only the curved length.

Given Data / Assumptions:

• Diameter D = 63 cm.
• Radius r = D/2 = 31.5 cm.
• Perimeter P = arc length (half circumference) + diameter.

Concept / Approach:Full circumference is 2 * pi * r. Half of that is pi * r. Therefore P = pi * r + D. Using pi = 22/7 works neatly with multiples of 7.

Step-by-Step Solution:

Verification / Alternative check:Compute half circumference as (pi * D)/2 + D = (22/7 * 63)/2 + 63 = (198)/2 + 63 = 99 + 63 = 162 cm. Same result confirms consistency.

Why Other Options Are Wrong:

• 132, 142, 172: Each misses the exact arithmetic from using pi = 22/7 with D divisible by 7. 132 would be the half circumference only if r were 42, which it is not.

Common Pitfalls:

• Forgetting to add the diameter after computing the arc.
• Using 2 * pi * r instead of pi * r for the arc portion.

Final Answer:162