Perimeter and Area
Lessons in this chapter
About Perimeter and Area
Perimeter and Area returns to 3rd grade’s two measurements with formulas attached and problems that run backwards.
Find the Area and Perimeter of Rectangles and Squares formalises what was counted by hand a year earlier. Area is length times width, perimeter is twice the length plus twice the width, and both formulas should be derived from the counting rather than handed over, so a child can rebuild a forgotten one.
Solve Real-World Problems on Area and Perimeter is where the work is. The useful problems run in reverse: given an area of 48 square meters and a width of 6, find the length. That turns the formula into an equation to solve, which is the first step towards algebra.
The chapter is also where it pays to keep showing that the two measurements are independent. Shapes with equal perimeters can have very different areas, and a child who has seen that will not substitute one formula for the other under pressure.
Both lessons open as a 4th grade math worksheet inside the page. Find the Area and Perimeter of Rectangles and Squares comes first, and Solve Real-World Problems on Area and Perimeter is a set of area and perimeter word problems, several of which run the formula backwards. Each question is scored as you answer it, free to try, with no login needed for your first 3.
Frequently asked questions
Find the Area and Perimeter of Rectangles and Squares formalises what was counted by hand in 3rd grade, with both formulas better derived from the counting than handed over. Solve Real-World Problems on Area and Perimeter is where the work is, and the useful problems run in reverse: given an area of 48 square meters and a width of 6, find the length. The chapter sits in the Common Core domain Measurement and Data (4.MD).
Area is length times width. Perimeter is twice the length plus twice the width, or add all four sides.
Divide. If the area is 48 and the width is 6, the length is 8. Running the formula backwards is what makes it an equation rather than a recipe.
Because both are calculated from the same two numbers. Keeping the units straight helps: perimeter is in meters, area is in square meters.
Yes. A 1 by 11 rectangle and a 6 by 6 square both have a perimeter of 24, but areas of 11 and 36. It is the clearest proof that they measure different things.
Area is side times side, and perimeter is four times the side. Both follow from the rectangle formulas, since a square is a rectangle with equal sides.