Area, Perimeter and Algebra

Updated – thanks to @JulieToddMath for spotting the mistake!

On Sunday evening, whilst following one link to another, I came across the Parent Guide PDF’s published on the College Preparatory Mathematics website. One of the things that caught my eye when I was looking through them was this problem:

AlgebraAreaPerimeterProblem

I really liked the idea of combining algebra work with area and perimeter, so I decided to make a couple of my own. This is something that works at so many different ability levels.

The first one I made for my year 11 class so they could practise their factorisation and expanding skills.

Algebra-Area and perimeter 1

Solution.

The second would be more appropriate for a year 12 class, as well as practising factorisation and expansion they also need polynomial division.

Algebra-Area and Perimeter 2

Solution.

If you like them, try making some yourself. How else could this idea be used?

Update:

Mr Calculator on Twitter suggested an alternative question to ask for the first problem: “If the area is 82, find x.”

With year 11 today I gave them them the top diagram, told them the area was 82, and asked them to find the perimeter.

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