The idea in brief. A figure with a piece taken out of it is TWO REGIONS. The one the question wants is the whole minus the piece that went. In the lesson. So the piece that is left is the whole, minus the piece that was cut out.
Lesson video, with the working
Area left when a circle is cut from a square
3 min 00 s
The film teaches 1 question. The question shows first; its working is written as the film explains it.
Question 1 of 22 · Basic · free to tryA wooden badge is made of a square of side 10 cm with a quadrant of radius…A wooden badge is made of a…
A wooden badge is made of a square of side 10 cm with a quadrant of radius 10 cm joined along one complete side. Find the total area of the badge. (Take π = 3.14.)
How do you find the area of composite figures with circles in P6?
This page covers figures made by joining shapes together or cutting one out of another, where at least one piece is a circle, semicircle or quarter circle.
What your child learns here
This page covers figures made by joining shapes together or cutting one out of another, where at least one piece is a circle, semicircle or quarter circle. It applies the Primary 6 outcome on composite figures made of squares, rectangles, triangles, semicircles and quarter circles.
Break a composite figure into shapes whose areas can be found one at a time.
Add the areas when shapes are joined, and subtract when one shape is removed from another.
Write the plan in words, such as area left equals square minus circle, before any numbers.
Find the area of a ring as the big circle's area minus the small circle's area.
Notice when four equal quarter circles fit together as one whole circle, and use that to save working.
Does the answer make sense?
When your child's figure has a circle or part of one cut out, or the shaded part lies inside a bigger shape, the answer must be smaller than that bigger shape. When pieces are only joined edge to edge, like a quarter circle on a square, the total must be larger than either piece.
How to practise these questions
Basic questions train adding whole shapes together, or subtracting a cut-out to find what is left, including rings between two circles. Intermediate questions add regions covered twice by overlapping quarter circles, and reading which parts are shaded or unshaded. Challenge questions find a difference between two regions neither of which can be measured alone, or paths of constant width with curved bends. When adding and subtracting circle pieces gets tangled, read the written step-by-step solution together.
Questions parents ask
What are composite figures in P6 maths? They are figures built from simpler shapes. The Primary 6 syllabus names square, rectangle, triangle, semicircle and quarter circle as the pieces, and asks for both the area and the perimeter of such figures.
How do I help my child find the area of a shaded region? Ask them to colour exactly the region the question asks for, then say in words how it is made: a whole shape plus another, or a whole shape minus a cut-out. The numbers go in only after that sentence is written.
How do you find the area of a ring between two circles? Find the area of the big circle and the area of the small circle, then subtract. It uses the Primary 6 circle area outcome twice, inside a composite figure.
