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Matthew from Parkgate Primary School focused on the first two shapes in the problem. He said:The area of the rectangle is $18$cm$^2$ and its perimeter is $18$cm.
Thomas from Colet Court examined the eight shapes which were drawn on the cards. He labelled the shapes A, B, C, D, E, F, G and H, going from left to right in the top row, then left to right in the bottom row.
Thomas didn't give any units in his solution. I guess we could say the perimeter is measured in 'units' and the area in 'square units', although some of you, like Matthew above, assumed the squares were 1cm long. So, that would mean the perimeter is in cm and the area in cm$^2$. Thomas remarked:The perimeter is always bigger except for one (Shape G).
Noor from Kingsbury Green Primary School answered the question; 'Can you draw a shape in which the area is numerically equal to its perimeter? And another?'. He said:I found if I did $4\times4$ I would get an area of $16$.
Table 3 (they didn't give their school) looked at finding a shape which has a perimeter numerically twice the area. They wrote:
Bashayer from Kingsbury Green Primary also found this solution. Miiti from Kingsbury Green created this shape which has a perimeter of $20$ units and an area of $10$ square units:
Thomas from Colet Court drew a shape in which the area is numerically twice the perimeter:
Thomas went on to investigate how to make the area of a shape go up but the perimeter go down. He said:
Thomas also said that you can make the perimeter of a shape go up but the area go downby inserting a dent in your shape the area gets reduced by the dent.
Sam and Lil from SMS summarised this by saying:
Joe and Charlie from Coniston Primary described the way they worked on this part of the problem:First we picked a shape which was a square so we looked at the area and perimeter.
Thomas also sent us shapes that have the same area but different perimeters:
and shapes that have the same perimeter but different areas:
Very, very well done all of you. You have obviously put a lot of thought into this problem.