The idea in brief. Cutting a circle MAKES NEW STRAIGHT EDGES. They were not there before, they are as much a part of the way round as the curve is, and they are the part that gets forgotten. In the lesson. Add the arc and the straight edges. That is the perimeter.
Lesson video, with the working
Perimeter of semicircles and quarter circles
3 min 41 s
The film teaches 2 questions in turn. Each question shows first; its working is written as the film explains it.
How do you find the perimeter of semicircles and quarter circles in P6?
When a circle is cut into a half, a quarter or another fraction, its perimeter is the curved arc plus the new straight edges the cut creates.
What your child learns here
When a circle is cut into a half, a quarter or another fraction, its perimeter is the curved arc plus the new straight edges the cut creates. This is Primary 6 outcome 1.2 on semicircles and quarter circles, and it is the building block for every composite perimeter question.
Find an arc as a fraction of the circumference: half for a semicircle, a quarter for a quarter circle, three quarters for a three-quarter piece.
Add the straight edges: one diameter for a semicircle, two radii for a quarter circle.
Give a perimeter in terms of pi when asked, such as 3 pi plus 12 cm for a quarter circle of radius 6 cm.
Work back from a given arc length to the radius of the circle it came from.
Does the answer make sense?
A semicircle's perimeter is a little more than two and a half times its diameter, and a quarter circle's a little more than three and a half times its radius, since the straight edges count as well. If your child's answer is close to the arc alone, those straight edges have been left out.
How to practise these questions
Basic questions train adding the straight edges to the arc: the two radii for a quarter, and the diameter for a semicircle. Intermediate questions add working back from an arc length to the radius, and three-quarter circles. Challenge questions put an arc in place of part of a side, or keep π as a symbol throughout. If a half or quarter perimeter comes out too short, read the written step-by-step solution together.
Questions parents ask
What is the perimeter of a semicircle? It is half the circumference plus the straight edge across the bottom, which is the diameter. In words: half of pi times the diameter, plus the diameter.
How do you find the perimeter of a quarter circle? Take a quarter of pi times the diameter for the curved edge, then add the two straight edges, which are both radii. For a radius of 10 cm, that is 15.7 plus 10 plus 10, or 35.7 cm.
What does 'leave your answer in terms of pi' mean? It means keep pi as a symbol and do not change it into 3.14 or 22/7. An answer such as 6 pi plus 12 cm is complete as it stands.
