Introduction
This PSLE Maths question tests your ability to calculate the perimeter of a semicircle, a common exam concept in PSLE Geometry. Students must combine radius, diameter, and curved length formulas accurately, especially when π is given as 3.14. In this worked example, our tutor shows how to correctly compute the curved edge + straight diameter to get the full perimeter.
The Question
The shaded figure is a semicircle of diameter 20 cm.
What is the perimeter of the shaded figure?
(Take \( \pi = 3.14 \))
Step-by-Step Working
Step 1 – Find the radius
\( r = \tfrac{20}{2} = 10 \,\text{cm} \)
Step 2 – Find semicircle circumference
Full circle: \( C = 2 \pi r = 2 \times 3.14 \times 10 = 62.8 \)
Half circle: \( \tfrac{62.8}{2} = 31.4 \,\text{cm} \)
Step 3 – Add the straight side
\( 31.4 + 20 = 51.4 \,\text{cm} \)
Final Answer
✅ Final Answer: \( \boxed{51.4 \,\text{cm}} \)
Correct Option: (2) 51.4 cm
Key Formula Recap
| Shape | Formula |
|---|---|
| Full circle | \( 2 \pi r \) |
| Semicircle (curved part) | \( \pi r \) |
| Perimeter of semicircle | \( \pi r + \text{diameter} \) |
Tips for Students
- Always divide diameter by 2 to get radius.
- A semicircle perimeter includes a straight edge, not just curve.
- Use the exact value of π given in the question.
For Parents
This topic strengthens spatial reasoning and formula application. We train students to avoid common traps such as:
- Forgetting to add diameter
- Using wrong π
- Using full circumference instead of half