The idea in brief. Where two shapes are joined, that edge is INSIDE the figure. It is not part of the way round, and a finger tracing the outside never touches it. In the lesson. The edge where the two shapes meet is inside the figure. So it is not counted.
Lesson video, with the working
Perimeter of a rectangle with a semicircle
2 min 33 s
The film teaches 1 question. The question shows first; its working is written as the film explains it.
A semicircle is joined to a rectangle. The rectangle is 20 cm long and 14 cm wide, and they join along one of the shorter sides. Find the perimeter of the whole figure. (Take π = 22/7.)
Perimeter = 22 + 20 + 14 + 20 = 76 cm
Ans: 76 cm
How to solve it
Go the whole way round and count only the sides on the outside. The edge where the two shapes meet is not on the perimeter.
Write the curve first, on its own line. It sits on the 14 centimetre side, so 14 is its diameter.
The arc is a half, times 22 over 7, times 14, which is 22 centimetres.
Write the straight edges in one line: the long side 20, the bottom 14 and the other long side 20.
Add the arc: 22 plus 20 plus 14 plus 20 is 76 centimetres.
The curve and the three straight sides are all counted. The edge where the two shapes meet is inside the figure. So it is not counted.
Practice questions with worked solutions
Question 1 is free to try. The other 21 open in the free trial, each with its full working.
Question 1 of 22 · Basic · free to tryA wooden name plaque is made of a rectangle 12 cm long and 5 cm wide, with a…A wooden name plaque is made of…
A wooden name plaque is made of a rectangle 12 cm long and 5 cm wide, with a semicircle of diameter 12 cm joined on top along the long side. Find the perimeter of the whole plaque. (Take π = 3.14.)
How do you find the perimeter of composite figures with semicircles in P6?
This page is about the distance round a figure made by joining rectangles or squares to semicircles and quarter circles.
What your child learns here
This page is about the distance round a figure made by joining rectangles or squares to semicircles and quarter circles. It applies the Primary 6 outcome on the perimeter of composite figures, where the key decision is which edges are on the outside and which are hidden inside.
Trace the outside of a composite figure and list every edge, curved or straight.
Find each curved edge as a fraction of pi times its own diameter.
Leave out any line where two shapes meet, because it lies inside the figure.
Write each arc on its own line when a figure has arcs of different sizes.
Recognise that a line drawn across a shaded region, such as a diameter, is not part of its boundary.
Does the answer make sense?
Your child's distance round each joined figure is in cm or m, never square units. A semicircle's curve is just over one and a half diameters, so a semicircle cut into or added onto a straight edge lengthens the outline, while rounding a corner with a quarter circle shortens it.
How to practise these questions
The Basic questions train walking only the outside edge of a shape, leaving out any line inside it. Intermediate questions add several arcs with different radii, rounded corners, and a lens-shaped overlap whose edge is made of two arcs. Challenge questions include bites and bumps on a side, a boundary made entirely of arcs, and working back from a given perimeter to a diameter. If walking round a combined shape is confusing, read the written step-by-step solution.
Questions parents ask
How do you find the perimeter of a shape with a semicircle? Find the curved edge as half of pi times its diameter, then add every straight edge on the outside of the figure. Leave out the side where the semicircle joins the rest of the shape, because it is inside.
Why is the joining line not part of the perimeter? Perimeter is the distance round the outside. Once two shapes are joined, the line between them is inside the figure, so a walk round the edge never touches it.
Is composite figure perimeter in the P6 syllabus? Yes. The Primary 6 syllabus includes finding the area and perimeter of composite figures made up of square, rectangle, triangle, semicircle and quarter circle.
