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Lesson 8 of 16
Perimeter of composite shapes
I can solve perimeter problems of composite shapes involving whole and/or part circles.
Lesson 8 of 16
New
New
Perimeter of composite shapes
I can solve perimeter problems of composite shapes involving whole and/or part circles.
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.
Doubling the angle of the sector does not double its perimeter. For example, a semicircle does not have double the perimeter of a quarter-circle with the same radius, as the lengths of the two radii bounding the arc have not doubled.
Teacher tip
Licence
This content is © Oak National Academy Limited (2025), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).
Lesson video
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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.
What is $${1\over4}$$ of 76$$\pi$$ cm? Give your answer in decimal form and rounded to 2 decimal places.
Correct Answer: 59.69 cm, 59.69cm
59.69 cm, 59.69cm
Q2.Which of these units of measurement is appropriate for measuring the perimeter of something?
Which of these units of measurement is appropriate for measuring the perimeter of something?
Correct answer: inches
inches
inches²
Correct answer: mm
mm
mm³
degrees
Q3.Which of these formulae finds the circumference of a circle with radius $$r$$ and diameter $$d$$?
Which of these formulae finds the circumference of a circle with radius $$r$$ and diameter $$d$$?
$$circumference = {\pi} {\times}r$$
Correct answer: $$circumference = 2{\times} {\pi} {\times}r$$
$$circumference = 2{\times} {\pi} {\times}r$$
Correct answer: $$circumference = {\pi} {\times}d$$
$$circumference = {\pi} {\times}d$$
$$circumference = {\pi} {\times}d^2$$
$$circumference = 2{\times}{\pi} {\times}d$$
Q4.Which of these describes the circumference of a circle with a diameter of 60 cm?
Which of these describes the circumference of a circle with a diameter of 60 cm?
30$$\pi$$ cm
Correct answer: 60$$\pi$$ cm
60$$\pi$$ cm
120$$\pi$$ cm
94.2 cm
Correct answer: 188.5 cm
188.5 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
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
Correct Answer: 20.9, 20.9 cm, 20.9cm
20.9, 20.9 cm, 20.9cm
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.
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.
Correct Answer: 110, 110 cm, 110cm
110, 110 cm, 110cm
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?
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?
Correct answer: 15$$\pi$$ cm
15$$\pi$$ cm
15$$\pi$$ + 30 cm
15$$\pi$$ + 60 cm
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?
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?
31$$\pi$$
97.4 cm
97.4 + 31 cm
Correct answer: 97.4 + 62 cm
97.4 + 62 cm
Correct answer: 159.4 cm
159.4 cm
Q3.Calculate the perimeter of this sector, giving your answer in cm and rounding your answer to 1 decimal place.
Calculate the perimeter of this sector, giving your answer in cm and rounding your answer to 1 decimal place.
Correct Answer: 294.8, 294.8 cm, 294.8cm
294.8, 294.8 cm, 294.8cm
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.
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.
There are three line segments of 68 cm.
Correct answer: There are four line segments of 68 cm.
There are four line segments of 68 cm.
There are five line segments of 68 cm.
The length of the arc is 68$$\pi$$ cm.
Correct answer: The length of the arc is 34$$\pi$$ cm.
The length of the arc is 34$$\pi$$ cm.
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.
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.
Correct Answer:value of $$a$$ ,9 cm
value of $$a$$ -
9 cm
Correct Answer:radius of each quarter-circle,8 cm
radius of each quarter-circle -
8 cm
Correct Answer:total length of line segments,34 cm
total length of line segments -
34 cm
Correct Answer:total length both arcs,8$$\pi$$ cm
total length both arcs -
8$$\pi$$ cm
Correct Answer:total perimeter of shape,59.1 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.
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.
Correct Answer: 216, 216 cm, 216cm
216, 216 cm, 216cm