Find Perimeter of Rectangles Using Formulas

Students will use efficient methods to find the perimeter of rectangles, including P = 2l + 2w and P = 2(l + w). They will apply these formulas and choose flexibly between them in mathematical and real-world contexts.

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Grade 3 · Perimeter of Polygons · question 1 of 3

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12 rungs. A star at the top.

Which shape has the greater perimeter?

How it is taught

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Perimeter is the distance around a shape.

A rectangle has two pairs of equal sides.

Read it: Walk the four sides

You have a 3 by 5 frame of squares. Counting every edge one by one is slow. The frame shows 15 inside and 16 around.

Walk the four sides of the frame: 5, 5, 3, 3.
Add them: 5 + 5 + 3 + 3 = 16 around.
Keep that apart from the inside count, which is 15.

Counting every tiny edge unit works, but it is slow and you lose track at the corners.

The 15 inside is how much space; the 16 around is how long the fence is.

Opposite sides match: two 5s and two 3s, so you add each pair once.

Add the four sides to walk around; the squares inside answer a different question.

Saying the walk around is 15 because there are 15 squares inside.

The 15 is the inside. Walk the four sides: 5 + 5 + 3 + 3 = 16.

A rectangle is 8 by 3. What is its perimeter? — 22. Walk around: 8 + 3 + 8 + 3 = 22.

Rectangle: length 8, width 5

Today we'll find the perimeter of a rectangle — the distance all the way around its edge.

Here's our rectangle. The long sides are 8 units, and the short sides are 5 units.

Grade 3 · Using P = 2l + 2w to find perimeter fast

We call the long side the length. Both lengths are the same — 8 and 8.

We call the short side the width. Both widths are also the same — 5 and 5.

Since opposite sides match, we can use a shortcut formula: P equals two times the length plus two times the width.

Plug in our numbers: two times 8, plus two times 5.

Two times 8 is 16. That's both lengths added together.

Two times 5 is 10. That's both widths added together.

Now add them: 16 plus 10 equals 26.

The perimeter is 26 units. The formula saved us from adding all four sides one by one. Nice work!

Now you try. Find the distance around this rectangle. How far around is it?

What you see

While they climb, your page writes one true line to ask about tonight, and a short note each Sunday.

MayaGrade 3 · Mathematics

Did you know?

A chessboard has 64 squares — share them out between the 8 rows and each row holds exactly 8.

Today’s goal: 1 star — one skill mastered, every rung of its ladder climbed
Climbing now: Divide within 100

An example student.

MayaGrade 3 · Mathematics

Maya earned 2 stars this week — Interpret multiplication as equal groups, which took 6 answers over 3 days before its star landed 3 days ago and Multiply by 6, 7, 8 and 9. Next up: Divide within 100.

An example week.

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