A semicircle has a radius of 28 centimetres. Using the standard formula for the perimeter of a semicircle, which includes the curved part and the diameter, find its total perimeter in centimetres. Take pi = 22/7.

Introduction / Context:
This problem checks your understanding of the perimeter of a semicircle, which is a very common shape in aptitude and geometry questions. The key idea is that the perimeter of a semicircle is not only the curved arc, but also includes the straight diameter. Forgetting the diameter is one of the most common mistakes in such problems.

Given Data / Assumptions:

• Radius of the semicircle r = 28 centimetres.
• We must find the total perimeter of the semicircle.
• Use pi = 22/7 for calculations.
• Perimeter means curved part plus the straight diameter.

Concept / Approach:
For a full circle, circumference = 2 * pi * r. For a semicircle, the curved part is half of the full circumference, which is pi * r. However, the perimeter of a semicircle also includes the diameter, which is 2 * r. Therefore, the perimeter P of a semicircle is given by:
P = pi * r + 2 * r.
We simply substitute the given radius and the given value of pi into this formula and compute the numerical value step by step.

Step-by-Step Solution:
Given r = 28 cm and pi = 22/7. Perimeter of semicircle P = pi * r + 2 * r. First compute pi * r: pi * r = (22/7) * 28. 28 divided by 7 is 4, so pi * r = 22 * 4 = 88. Now compute the diameter term: 2 * r = 2 * 28 = 56. Add both contributions: P = 88 + 56 = 144. Therefore, the perimeter of the semicircle is 144 centimetres.

Verification / Alternative check:
We can quickly check the reasonableness of the answer. A full circle of radius 28 cm would have circumference 2 * pi * r = 2 * (22/7) * 28 = 176 cm. A semicircle will have slightly less than this value as its total perimeter, since it has half the circumference (88) plus one diameter (56), giving 144, which is less than 176 but more than the half circumference 88. The number 144 therefore makes sense in this context.

Why Other Options Are Wrong:
Option A (242): This is larger than the circumference of the full circle, so it cannot be the perimeter of a semicircle. Option C (121): This does not match pi * r + 2 * r and comes from no standard combination of radius and pi. Option D (288): This is exactly double the correct value and might result from mistakenly using 2 * (pi * r + 2 * r). Option E (200): This is an arbitrary incorrect value and does not match the correct formula.

Common Pitfalls:
The biggest pitfall is using only the curved part of the semicircle and forgetting to add the diameter, which would give 88 instead of 144. Another common issue is using the wrong formula, such as 2 * pi * r for a semicircle. Some students also make arithmetic errors when multiplying by 22/7. Writing out each step clearly and remembering that a semicircle has both a curved boundary and a straight boundary helps avoid errors.

Final Answer:
The perimeter of the semicircle is 144 centimetres.