Area and perimeter of four shapes

Area and perimeter of four shapes

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This task is about finding the shape with the largest area and longest perimeter.
Shapes A to D are made up of identical equilateral triangles.
The three sides of each triangle are each 1 cm long.
 
shape A made using triangles
Shape A
 
shape B made using triangles
Shape B
 
shape C made using triangles
Shape C
shape D made using triangles
Shape D
 

Question

a)  Which of the shapes has the largest area?

    • shapeA.png

    • shapeB.png

    • shapeC.png

    • shapeD.png

    • All the shapes have the same area

Question

b)  Which of the shapes has the longest perimeter?

    • shapeA.png

    • shapeB.png

    • shapeC.png

    • shapeD.png

    • All the shapes have the same perimeter

Task administration: 
This task can be completed online and has auto marking displayed to students.
Level:
4
Curriculum info: 
Maths, Geometry and Measurement, Measurement
Key Competencies: 
Thinking
Keywords: 
area, perimeter
Description of task: 
Students identify which of four shapes created from equilateral triangles has the largest area and which has the largest perimeter.
Curriculum Links: 
This resource can help to identify students' understanding of area and perimeter.
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 (06/2000)

a)

All the shapes have the same area

easy

b)

Area-perimeter-shapeB.png

moderate
 
Diagnostic and formative information: 
 

Common error

Likely reason

b)

35% of students selected option

Area-perimeter-shapeC.png

Confused longest perimeter with longest shape.
Next steps: 
Extension  

  1. Draw shapes with the ten equilateral triangles with as many possible perimeters as you can. The triangles must either touch just at a vertex or have one side wholly in common. (All even numbers between 8 and 30 have solutions)
  2. What is the maximum possible perimeter? (Answer: 30 cm).