Perimeter of composite shapes
I can solve perimeter problems of composite shapes involving whole and/or part circles.
Perimeter of composite shapes
I can solve perimeter problems of composite shapes involving whole and/or part circles.
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Lesson details
Key learning points
- The length of fractions of the circumference of a circle can be found.
- The perimeter of parts of a circle can be found using the formula for the circumference and reasoning.
- The perimeter of shapes made from circles and parts of circles can be found using the circumference and reasoning.
- The perimeter of composite shapes including circles can be found.
Keywords
Arc - An arc is part of a curve. When describing an arc of a circle, it is part of the circle's circumference.
Common misconception
Shapes with the same area also have the same perimeter.
Demonstrate that component parts being rearranged has no effect on its area, but may affect its perimeter.
To help you plan your year 8 maths lesson on: Perimeter of composite shapes, download all teaching resources for free and adapt to suit your pupils' needs...
To help you plan your year 8 maths lesson on: Perimeter of composite shapes, download all teaching resources for free and adapt to suit your pupils' needs.
The starter quiz will activate and check your pupils' prior knowledge, with versions available both with and without answers in PDF format.
We use learning cycles to break down learning into key concepts or ideas linked to the learning outcome. Each learning cycle features explanations with checks for understanding and practice tasks with feedback. All of this is found in our slide decks, ready for you to download and edit. The practice tasks are also available as printable worksheets and some lessons have additional materials with extra material you might need for teaching the lesson.
The assessment exit quiz will test your pupils' understanding of the key learning points.
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Explore more key stage 3 maths lessons from the Perimeter, area and volume unit, dive into the full secondary maths curriculum, or learn more about lesson planning.
Licence
Prior knowledge starter quiz
6 Questions
Q1.What is $${1\over4}$$ of 76$$\pi$$ cm? Give your answer in decimal form and rounded to 2 decimal places.
Q2.Which of these units of measurement is appropriate for measuring the perimeter of something?
Q3.Which of these formulae finds the circumference of a circle with radius $$r$$ and diameter $$d$$?
Q4.Which of these describes the circumference of a circle with a diameter of 60 cm?
Q5.A circular hoop with a radius of 40 cm is cut into 12 equally-sized pieces. What is the length of one piece? Give your answer in cm, rounded to 1 decimal place. cm
Q6.Circle A has a radius of 49 cm. Circle B has a diameter of 1.33 metres. How much longer is the circumference of circle B than circle A? Give your answer in cm, rounded to the nearest integer.
Assessment exit quiz
6 Questions
Q1.A quarter-circular sector is cut out of a circle. The original circle had a perimeter of 60$$\pi$$ cm. What is the arc length of this sector?
Q2.A semicircular sector is cut out of a circle. The radius of the original circle is 31 cm, and its circumference is 194.8 cm (rounded to 1 decimal place). What is the perimeter of the sector?
Q3.Calculate the perimeter of this sector, giving your answer in cm and rounding your answer to 1 decimal place.

Q4.This composite shape is composed of a circular sector and a square. Which of these statements are true about the perimeter of this composite shape that has been broken into component lengths.

Q5.This composite shape is composed of two quarter-circles and a rectangle. Match the statement about the component parts of the composite shape's perimeter to the correct value.

value of $$a$$ -
9 cm
radius of each quarter-circle -
8 cm
total length of line segments -
34 cm
total length both arcs -
8$$\pi$$ cm
total perimeter of shape -
59.1 cm
Q6.The square at the centre of this composite shape has an area of 441 cm². Find the perimeter of the composite shape in cm, rounded to the nearest integer.
