Quad Areas

Topics: Starter | Area | Geometry | Investigations | Mensuration | Shape

• CB, Kent
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• I can find ☆ ☆ different quadrilaterals (if you're allowed to count Big Square and Small Square). Areas - two ☆ s, two ☆ . ☆ s, four ☆ s, one ☆ , one ☆ . Can't find the ☆ . ☆ at all. Am I missing something really obvious?
• 8K3, Kettlethorpe High School
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• We found ☆ ☆ which included the area of ☆ . ☆ . ( ☆☆☆ ☆☆☆ ☆☆☆ ).
• Snev, Holy Trinity, Crawley
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• There are ☆ ☆ different quadrilaterals and their total area is ☆ ☆ . ☆ cm ^☆ assuming the dots are ☆ cm apart. ( ☆ x ☆ )( ☆ x ☆ . ☆ )( ☆ x ☆ )( ☆ x ☆ . ☆ )( ☆ x ☆ )( ☆ x ☆ ). The ☆ . ☆ cm ^☆ quadrilateral joins dots ☆ , ☆ , ☆ and ☆ .
• Louise And Laura., Carnoustie High School
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• The problem was very challenging and we all enjoyed it. It was more challenging than Friday's.
• Claire, Sam And Mr A, Alcester High School
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• We found ☆ ☆ quadrilaterals, ( ☆ x ☆ )( ☆ x ☆ )( ☆ x ☆ . ☆ )( ☆ x ☆ . ☆ )( ☆ x ☆ )( ☆ x ☆ )
  Only took us ☆ minutes too (-ish!).
• Nairn Spink, 2AY2, High School Of Dundee
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• We really enjoyed it and I thought it really got us thinking, we are really pleased to do all the staters of the day
  thanks
  :).
• Yr 8 Tops, Rego School
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• There should be quite a lot. My class managed about ☆ ☆ so far.
• Yr9 QTY, West Island School, Hong Kong
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• We enjoyed this - it kept us occupied for over ☆ ☆ mins.
• Mrbeer, Essex
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• Surely with a parallelogram that crosses over the diagonals, the area is root ☆ = ☆ . ☆ ☆ ?
• Charles, Chelsea
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• My class found about ☆ ☆ ☆ wow.
• A And F, Dps
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• Our team got ☆ ☆ different ways.
• Jelissa, Massachusetts
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• It would be great if each quadrilateral could keep its own individual color, for a visual.
• Steve, Carlsbad, CA
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• There are:
  ☆ ☆ convex quadrilaterals (not including the triangles)
  ☆ ☆ simple non-convex quadrilaterals
  ☆ ☆ triangles with an extra vertex on the midpoint of one side
  ☆ ☆ degenerate quadrilaterals where one edge overlays half of an adjacent edge
  ☆ ☆ ☆ complex quadrilaterals where two opposite sides intersect each other in a fifth point that is not a vertex of the quadrilateral
  The total number of quadrilaterals is ☆ ☆ ☆ , which is ☆ ☆ ☆ ways to choose four vertices from nine possible points times three ways to arrange any of four vertices into a ring.
  The possible areas for the convex quadrilaterals are ☆ , ☆ . ☆ , ☆ , ☆ . ☆ , ☆ or ☆ .
  The possible areas for the nonconvex quadrilaterals are ☆ or ☆ . ☆ .
  The possible areas for the triangles are ☆ or ☆ .
  The possible areas for the degenerate quadrilaterals ☆ . ☆ or ☆ (because it is half of the area of the corresponding triangle).
  The area of a complex quadrilateral is defined as the difference between the areas of the two triangles that are created. The possible areas for the complex quadrilaterals are ☆ , ☆ . ☆ or ☆ .

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