Quad Areas

A Mathematics Lesson Starter Of The Day

Calculate the areas of all the possible quadrilaterals that can be constructed by joining together dots on this grid:

Teacher: Click on the dots above to show joining lines. Assume that the vertical and horizontal distances between adjacent dots is one unit.

A printable sheet for student use is available here.


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

  • CB, Kent
  • I can find 10 different quadrilaterals (if you're allowed to count Big Square and Small Square). Areas - two 1s, two 1.5s, four 2s, one 3, one 4. Can't find the 2.5 at all. Am I missing something really obvious?
  • 8K3, Kettlethorpe High School
  • We found 11 which included the area of 2.5. (top left to top right to middle right to bottom middle to top left).
  • Snev, Holy Trinity, Crawley
  • There are 14 different quadrilaterals and their total area is 31.5 cm2 assuming the dots are 1 cm apart. (2x1)(4x1.5)(5x2)(1x2.5)(1x3)(1x4). The 2.5 cm2 quadrilateral joins dots 1,2,6 and 7.
  • Louise And Laura., Carnoustie High School
  • 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
  • We found 16 quadrilaterals, (5x1)(5x2)(3x1.5)(1x2.5)(1x3)(1x4)
    Only took us 3 minutes too (-ish!).
  • Nairn Spink, 2AY2, High School Of Dundee
  • We really enjoyed it and I thought it really got us thinking, we are really pleased to do all the staters of the day
  • Yr 8 Tops, Rego School
  • There should be quite a lot. My class managed about 30 so far.
  • Yr9 QTY, West Island School, Hong Kong
  • We enjoyed this - it kept us occupied for over 15mins.
  • Mrbeer, Essex
  • Surely with a parallelogram that crosses over the diagonals, the area is root 5 = 2.23?
  • Charles, Chelsea
  • My class found about 167 wow.
  • A And F, Dps
  • Our team got 32 different ways.
  • Jelissa, Massachusetts
  • It would be great if each quadrilateral could keep its own individual color, for a visual.

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