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Area and Perimeter Worksheets

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Count unit squares, tile rectangles, multiply side lengths, split L shapes, find perimeters and unknown sides, and compare rectangles. With answer keys.

Download the area and perimeter worksheets

Area: count squares and tile

An area and perimeter chart, counting unit squares in rectangles and other shapes, and finishing the tiling of a rectangle to see rows times columns.

Area: multiply and add

Multiply side lengths to find the area of rectangles, split L shapes into two rectangles and add, show the distributive property with area, and solve area word problems.

  • Preview of the printable “Area of Rectangles, sheet A” worksheet: multiplying side lengths to find the area of rectangles in centimeters and inchesView all 2 pages

    Area of Rectangles, sheet A

    Multiplying side lengths to find the area of rectangles in centimeters and inches

    Answer key on page 2

    US LetterPDFA4PDF

    2 pages35 KB

  • Preview of the printable “Area of Rectangles, sheet B” worksheet: multiplying side lengths to find the area of rectangles and squares in feet, meters, yards and inchesView all 2 pages

    Area of Rectangles, sheet B

    Multiplying side lengths to find the area of rectangles and squares in feet, meters, yards and inches

    Answer key on page 2

    US LetterPDFA4PDF

    2 pages35 KB

  • Preview of the printable “Area of rectilinear Figures, sheet A” worksheet: splitting L shapes on a grid into two rectangles and adding the areasView all 2 pages

    Area of rectilinear Figures, sheet A

    Splitting L shapes on a grid into two rectangles and adding the areas

    Answer key on page 2

    US LetterPDFA4PDF

    2 pages35 KB

  • Preview of the printable “Area of rectilinear Figures, sheet B” worksheet: finding the area of L shapes from side lengths by splitting them into rectanglesView all 2 pages

    Area of rectilinear Figures, sheet B

    Finding the area of L shapes from side lengths by splitting them into rectangles

    Answer key on page 2

    US LetterPDFA4PDF

    2 pages35 KB

  • Preview of the printable “Area and the distributive property” worksheet: splitting a rectangle into two to show a × (b + c) = a × b + a × cView all 2 pages

    Area and the distributive property

    Splitting a rectangle into two to show a × (b + c) = a × b + a × c

    Answer key on page 2

    US LetterPDFA4PDF

    2 pages41 KB

Perimeter

Count unit lengths around shapes on a grid, add side lengths of polygons drawn to proportion, and use the perimeter to find an unknown side.

  • Preview of the printable “Perimeter of Polygons, sheet A” worksheet: adding side lengths to find the perimeter of rectangles, squares, triangles and trapezoidsView all 2 pages

    Perimeter of Polygons, sheet A

    Adding side lengths to find the perimeter of rectangles, squares, triangles and trapezoids

    Answer key on page 2

    US LetterPDFA4PDF

    2 pages33 KB

  • Preview of the printable “Perimeter of Polygons, sheet B” worksheet: adding side lengths to find the perimeter of hexagons, pentagons, trapezoids and rectilinear shapesView all 2 pages

    Perimeter of Polygons, sheet B

    Adding side lengths to find the perimeter of hexagons, pentagons, trapezoids and rectilinear shapes

    Answer key on page 2

    US LetterPDFA4PDF

    2 pages35 KB

Area and perimeter together

Draw rectangles with the same area, compare rectangles with the same perimeter or the same area, and decide whether a word problem needs area or perimeter.

  • Preview of the printable “Draw rectangles with an area” worksheet: drawing different rectangles with the same area on grid paper and labeling the sidesView all 2 pages

    Draw rectangles with an area

    Drawing different rectangles with the same area on grid paper and labeling the sides

    Answer key on page 2

    US LetterPDFA4PDF

    2 pages34 KB

  • Preview of the printable “Same Perimeter, different area” worksheet: finding that rectangles with the same perimeter can have different areasView all 2 pages

    Same Perimeter, different area

    Finding that rectangles with the same perimeter can have different areas

    Answer key on page 2

    US LetterPDFA4PDF

    2 pages47 KB

  • Preview of the printable “Same Area, different perimeter” worksheet: finding that rectangles with the same area can have different perimetersView all 2 pages

    Same Area, different perimeter

    Finding that rectangles with the same area can have different perimeters

    Answer key on page 2

    US LetterPDFA4PDF

    2 pages44 KB

  • Preview of the printable “Area and perimeter word problems” worksheet: deciding whether a problem asks for area or perimeter, then solving itView all 2 pages

    Area and perimeter word problems

    Deciding whether a problem asks for area or perimeter, then solving it

    Answer key on page 2

    US LetterPDFA4PDF

    2 pages42 KB

Print at 100% (actual size) for the cleanest tracing lines.

About these area and perimeter worksheets

Area is the amount of space inside a flat shape, measured in square units. Perimeter is the distance around it, measured in units of length. Third graders learn both, and learn to tell them apart: a rug covers an area, a fence goes around a perimeter.

These worksheets start with counting unit squares and finishing the tiling of rectangles, so children see why the area of a rectangle is length times width. Then they multiply side lengths, split L shapes into two rectangles and add, and use area to show the distributive property. The perimeter pages count unit lengths on a grid, add side lengths, and use a known perimeter to find a missing side.

Grids are drawn with exact unit squares, and polygons with side lengths are drawn to proportion, so a 6 cm side really is longer than a 3 cm side. The last pages compare rectangles with the same perimeter or the same area. Every practice page has an answer key on page 2.

Standards

  • CCSS.MATH.CONTENT.3.MD.C.5Recognize area as an attribute of plane figures and understand concepts of area measurement.
  • CCSS.MATH.CONTENT.3.MD.C.6Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units).
  • CCSS.MATH.CONTENT.3.MD.C.7.AFind the area of a rectangle with whole-number side lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths.
  • CCSS.MATH.CONTENT.3.MD.C.7.BMultiply side lengths to find areas of rectangles with whole-number side lengths in the context of solving real world and mathematical problems, and represent whole-number products as rectangular areas in mathematical reasoning.
  • CCSS.MATH.CONTENT.3.MD.C.7.CUse tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a × b and a × c. Use area models to represent the distributive property in mathematical reasoning.
  • CCSS.MATH.CONTENT.3.MD.C.7.DRecognize area as additive. Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts, applying this technique to solve real world problems.
  • CCSS.MATH.CONTENT.3.MD.D.8Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters.

How to use them

  1. Start with the Area and Perimeter Chart and talk about covering versus going around.
  2. Use Area: Count the Squares and Tile the Rectangle before Area of Rectangles, so the multiplication makes sense.
  3. Area of Rectilinear Figures Sheet A is on a grid; Sheet B gives only side lengths.
  4. Use Perimeter on a Grid before Perimeter of Polygons, then Find the Unknown Side.
  5. Finish with the same perimeter and same area pages and the mixed word problems.

Teaching tips

  • Write the unit every time: square centimeters for area, centimeters for perimeter.
  • When counting perimeter on a grid, count the edges, not the squares. Corner squares have two outside edges.
  • For L shapes, draw the split line first and label both rectangles before multiplying.
  • Rectangles with the same perimeter can have different areas. The one closest to a square has the most area.

Questions teachers and parents ask

What is the difference between area and perimeter?

Area is the space inside a shape, counted in square units. Perimeter is the distance around the outside, counted in units of length like centimeters or feet.

How do 3rd graders find area?

First by counting unit squares, then by tiling a rectangle and seeing it is rows times columns. Then they multiply the side lengths, and add the areas of rectangles to find the area of L shapes.

How do you find an unknown side from the perimeter?

Add the sides you know, then subtract that total from the perimeter. For a rectangle you only need two sides, because opposite sides are equal.