Same area, different lengths

Same area, different lengths

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This task is about working out the width and perimeter for different shapes with the same area.

Question 1Change answer

A rectangle has an area of 84 cm2.

Several rectangles can be drawn all with an area of 84 cm2 but with different perimeters.

Complete the table below showing the width and perimeter of three rectangles all with an area of 84 cm2 and the given length.

 

Length (cm)

Width (cm)

Perimeter (cm)


a)

42

i)     

ii)     


b)

14

i)     

ii)     


c)

12

i)     

ii)     

 

Task administration: 
This task can be completed with pencil and paper or online with auto-marking.
Level:
4
Curriculum info: 
Maths, Geometry and Measurement, Measurement
Keywords: 
area, perimeter, rectangles
Description of task: 
Students find the width and perimeter of three rectangles with the same area and different lengths.
Curriculum Links: 
This resource can help to identify students' understanding of calculating perimeter and area.
Learning Progression Frameworks
This resource can provide evidence of learning associated with
Measurement sense, sets 6-7
within the Mathematics Learning Progressions Frameworks.
Read more about the Learning Progressions Frameworks.
Answers/responses: 
  

Y8 (07/1997)
a) i)
ii)		 2
88		 moderate
difficult
b) i)
ii)		 6
40		 moderate
difficult
c) i)
ii)		 7
38		 moderate
difficult
 
NOTE: For part ii) accept answer if perimeter = 2 × w + 2 × l.