Area and perimeter problems: rectangles and rectangular shapes

This is a problem solving lesson in which we solve several problems involving both area and perimeter of rectangles or rectangular shapes. It is suited to grades 3-5.

The first problem involves a shape that we can divide into several rectangles, and then figure its area and perimeter. Some side lengths are missing — but we can find those by subtracting.

Then our task is to draw rectangles with an area of 20 square units. There are several, of course. I write in the table their side lengths, and then we also calculate the perimeter of each. We notice how the skinniest rectangle has the largest perimeter, and the rectangle that is closes to a square has the least perimeter (of these three)!

Our last problem is almost like a puzzle — draw a rectangle with an area of 60 square units and a perimeter of 34 units. Guess and check helps!

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See also

Math Mammoth Early Geometry — a self-teaching worktext with explanations & exercises for beginning geometry topics (grades 1-3)

Math Mammoth Grade 3 complete curriculum

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