Perimeter of composite shapes | Maths | Quizalize & Oak National Academy

Starter quiz

What is ${1\over4}$ of 76 $\pi$ cm? Give your answer in decimal form and rounded to 2 decimal places. ______
- '59.69 cm' ✓
Which of these units of measurement is appropriate for measuring the perimeter of something?
- inches ✓
- inches²
- mm ✓
- mm³
- degrees
Which of these formulae finds the circumference of a circle with radius $r$ and diameter $d$ ?
- $circumference = {\pi} {\times}r$
- $circumference = 2{\times} {\pi} {\times}r$ ✓
- $circumference = {\pi} {\times}d$ ✓
- $circumference = {\pi} {\times}d^2$
- $circumference = 2{\times}{\pi} {\times}d$
Which of these describes the circumference of a circle with a diameter of 60 cm?
- 30 $\pi$ cm
- 60 $\pi$ cm ✓
- 120 $\pi$ cm
- 94.2 cm
- 188.5 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
- '20.9' ✓
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.
- '110' ✓

Exit quiz

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?
- 15 $\pi$ cm ✓
- 15 $\pi$ + 30 cm
- 15 $\pi$ + 60 cm
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
- 97.4 + 62 cm ✓
- 159.4 cm ✓
Calculate the perimeter of this sector, giving your answer in cm and rounding your answer to 1 decimal place.
- '294.8' ✓
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.
- 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.
- The length of the arc is 34 $\pi$ cm. ✓
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 ✓
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.
- '216' ✓

Worksheet

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Presentation

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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.

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.

Keywords

Arc - An arc is part of a curve. When describing an arc of a circle, it is part of the circle's circumference.