Grade 3 · Math · 2 minutes
Area vs perimeter: what's the difference?
Perimeter: add the sides. Area: count the squares.
Key terms
- Perimeter
- The distance around the outside edge of a shape, found by adding up every side.
- Area
- The amount of space inside a shape, found by counting the squares that cover it.
- Square foot
- A square that is one foot on every side, used to measure area.
- Length
- How long a rectangle is, which you multiply by the width to find the area.
- Width
- How wide a rectangle is, which you multiply by the length to find the area.
Transcript
Your puppy needs a new play yard. You'll need a fence to go around it, and grass to cover the inside. How much fence? How much grass? Those are two different questions, with two different answers.
Start with the fence. This yard is six feet long and two feet wide. Walk all the way around the edge, and add up every side. Six plus two plus six plus two is sixteen. Sixteen feet of fence. That distance around the outside is called the perimeter.
Now the grass. Imagine it comes in square tiles, each one foot on every side. One square foot. Cover the whole inside, with no gaps and no overlaps, then count them up. Twelve squares. The amount of space inside is called the area: twelve square feet.
Counting works, but here is a shortcut. The squares sit in two rows of six. Two times six is twelve. For a rectangle, multiply the length by the width, and you get the area.
Now, a puzzle. Take the same sixteen feet of fence and reshape it into a square, four feet on each side. Four plus four plus four plus four. The perimeter is still sixteen feet. But four rows of four make sixteen square feet of grass, up from twelve. Same fence, more room for zoomies!
So how do you remember which is which? Look inside the word perimeter. See the word rim? The perimeter is the rim, the edge around the outside. And area is all the space the shape covers.
So remember. Perimeter is the distance around: add the sides. Area is the space inside: count the squares, or for a rectangle, multiply length by width. And shapes with the same perimeter can have different areas. Just ask the puppy.
Sources
Every fact in the video, and where it comes from.
- 1mathsisfun.com/geometry/perimeter.html
- Perimeter is the distance around a two-dimensional shape; for a rectangle you can add all four side lengths (or 2 × (a + b)).
- Worked example 1 (invented for teaching; own calculation, the linked page gives the method only): a rectangle 6 feet by 2 feet has perimeter 6 + 2 + 6 + 2 = 16 feet and area 2 × 6 = 12 square feet (2 rows of 6 unit squares).
- 2mathsisfun.com/geometry/area.html
- Area is the size of a surface; it can be found by putting the shape on a grid and counting squares, and for a rectangle Area = w × h.
- Worked example 2 (invented for teaching; own calculation, the linked page gives the method only): a square 4 feet on each side has perimeter 4 + 4 + 4 + 4 = 16 feet and area 4 × 4 = 16 square feet, so the same perimeter as example 1 encloses a larger area.
- 3thecorestandards.org/Math/Content/3/MD
- CCSS 3.MD.C.5: a square with side length 1 unit, a 'unit square', has 'one square unit' of area; a plane figure which can be covered without gaps or overlaps by n unit squares has an area of n square units. 3.MD.C.6: measure areas by counting unit squares. 3.MD.C.7a/b: find the area of a rectangle by tiling it and show it is the same as multiplying the side lengths.
- CCSS 3.MD.D.8 (Grade 3): solve problems involving perimeters of polygons, including 'exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters'.
- 4en.wikipedia.org/wiki/Perimeter
- The word perimeter comes from Greek peri ('around') + metron ('measure'). (Background only. The 'rim' memory trick in the video is a spelling trick, not the word's origin: the letters r-i-m appear inside pe-RIM-eter.)
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