Area and Perimeter Worksheets

Area and perimeter are the two ways to measure a flat shape: area tells how much surface it covers, and perimeter tells how far it is around the edge. The eight PDFs on this page start with counting squares on a grid and move on to rectangles and missing sides, and every sheet has an answer key. They follow standards 3.MD.C.5 to 3.MD.C.7 and 3.MD.D.8 of the Common Core standards for grade 3 measurement and data, and the notes below add tables, worked examples and a plan to the formulas.

From counting squares to multiplying

Area starts with counting: every square on the grid is 1 square unit. Children soon notice that a rectangle with 4 rows of 6 squares has 4 × 6 = 24 squares, which is the area formula (length × width). Perimeter is the total length around the edge: for a rectangle, add all four sides, or double the length plus the width.

• Area on a grid: count the shaded squares, including L-shapes.
• Area and perimeter on a grid: count squares and outside edges.
• Rectangles: use the side lengths to find area and perimeter.
• Missing side: the area is 36 sq cm and one side is 4 cm; what is the other side?

Formulas for rectangles and squares

Worked examples

• A rectangle 7 cm long and 3 cm wide: area = 7 × 3 = 21 sq cm; perimeter = 2 × (7 + 3) = 20 cm.
• A square with sides of 5 m: area = 25 sq m; perimeter = 20 m.
• L-shape: a 6 × 4 rectangle with a 2 × 2 square cut from one corner. Area = 24 − 4 = 20 sq units. The perimeter stays 20 units, the same as the full rectangle, because the cut-out corner swaps two edges for two edges of the same length.
• Missing side: the area is 36 sq cm and one side is 4 cm, so the other side is 36 ÷ 4 = 9 cm.

Area or perimeter? A memory trick

Perimeter is the fence around a field; area is the grass inside it. Perimeter is measured in units of length (cm, m); area in square units (sq cm, m²).

Try this activity

Give children 20 squares (or 20 cm of string for the perimeter). Which rectangles can they make with a perimeter of 20? 1 × 9 (area 9), 2 × 8 (16), 3 × 7 (21), 4 × 6 (24) and 5 × 5 (25). The square gives the biggest area, a result that surprises most classes.

Common mistakes

• Adding only two sides for the perimeter.
• Writing cm instead of sq cm for area.
• Counting the corner squares twice when finding the perimeter on a grid.

Area and perimeter worksheets: what is in the set

There are 8 area and perimeter worksheets on this page, and every one has an answer key except for any cut-out games. Four sheets use grids, and the other four use the side lengths of rectangles, with two sheets that find a missing side.

Area worksheets grade 3: counting squares first

The area worksheets grade 3 start with counting, because area means “how many unit squares fit inside”. Wikipedia’s article on area explains that area is always measured in square units. A child who counts the squares of a shape learns that the area of a rectangle is the number of rows times the number of columns, before they meet the formula. This table shows six shapes on a grid, with the area and the perimeter counted from the squares:

Shapes that are not rectangles, such as the L-shape and the staircase, can still have their area counted. The perimeter of the staircase is the same as the perimeter of the 4 by 4 square around it, which is 16. The plus sign has 5 squares, and its perimeter is more than twice as big, at 12. The multiplication arrays and equal groups page shows how the rows and columns of an array lead to multiplication.

Perimeter worksheets: walking around the edge

The perimeter worksheets ask children to walk around the edge of a shape and add up the lengths of the sides. For a rectangle, two sides are the length and two are the width, so the perimeter is 2 × (length + width). Wikipedia’s article on the perimeter shows the same idea for many shapes. The most surprising fact is that rectangles with the same perimeter can hold very different amounts. This table shows all the rectangles with whole-number sides and a perimeter of 20:

The area goes up from 9 to 25 as the rectangle gets closer to a square, and the square has the greatest area. The opposite is also true: rectangles with the same area can have very different perimeters. This table shows the four rectangles with an area of 24:

The thin 1 by 24 rectangle needs 50 units of fence, and the 4 by 6 rectangle needs only 20. This is why farmers and builders use shapes that are close to a square.

Area of rectangles worksheets: length times width

The area of rectangles worksheets use the side lengths instead of a grid, so the formula length × width is needed. Each square unit in the rectangle is one in a row of length squares, and there are width rows. This table shows six rectangles with both the area and the perimeter:

The area and the perimeter can be compared only for the numbers, not for the meaning, since one is in square units and the other in units of length. If both sides of a rectangle are doubled, the perimeter doubles but the area becomes four times as big, as this table shows:

Counting squares area: composite shapes and the L-shape

For counting squares area in an L-shape, there are two ways to find the area without counting every square. One way is to split the shape into two rectangles and add. The other is to take a smaller rectangle away from a bigger one, as in 6 × 4 − 2 × 2 = 20. The perimeter of an L-shape is a surprise: it is the same as the perimeter of the outer rectangle. This table shows five examples:

The cut-out corner removes two edges from the outside, but adds two edges of the same length on the inside, so the perimeter does not change. This works for any corner that is cut out of a rectangle, which makes a good question for a class.

Missing side: using the area to find a side

The worksheets that find the missing side use the area and one side of a rectangle to find the other side. Since area = length × width, the missing side is the area divided by the side that is known. This is a use of division facts, and the times tables worksheets page has the facts. This table shows five problems, and the perimeter of each rectangle once the side is found:

Squares: how area and perimeter grow

A square has equal sides, so its area is side × side and its perimeter is 4 × side. As the side grows, the area grows much faster than the perimeter. This table shows the squares from 1 to 8:

A square of side 4 is special, since its area and perimeter are both 16. For smaller squares the perimeter is bigger, and for bigger squares the area is bigger. Because area and perimeter have different units, this is just a number fact, but it is a good puzzle.

Square units: why area has its own units

Area is measured in square units, such as square centimeters, which are written sq cm or cm². A square unit is a square with sides of one unit. When the unit of length changes, the square unit changes by the square of the factor. This table shows four examples:

This is the reason why changing between square units is harder than changing between units of length. The converting units page has the conversions for length, weight, capacity and time.

Where area and perimeter are used

Every job that involves covering or surrounding a shape uses area or perimeter. This table shows six jobs and which one each uses:

The perimeter and area calculator checks answers for rectangles and other shapes, and the geometry worksheets pages show the shapes themselves. The two measures come back in grade 4, where children use the formulas to solve problems in standard 4.MD.A.3, and in grade 6, where they find areas of triangles and other polygons.

More common mistakes with area and perimeter

The mistakes below add to the list above. They come up most with rectangles and with L-shapes. This table shows five of them, what went wrong and the fix:

Area and perimeter word problems

Area and perimeter come up in gardens, rooms and posters. Ask children to draw the shape, label the sides, and say whether the question is about area or perimeter:

Games and activities for area and perimeter

Children learn area and perimeter best when they play with it. These games use things that are found at home or in a classroom:

• Fence the field: give each child 20 cm of string, and ask them to find the rectangle with the most area
• Tile a floor: cover a rectangle on grid paper with square tiles, and count them
• Same area, new shape: find as many rectangles with an area of 24 as you can, and write their perimeters
• Playground sketch: draw a plan of a playground on grid paper, and find its area and perimeter
• L-shape challenge: cut a corner from a rectangle, and find the area and perimeter before and after
• Area and perimeter bingo: a bingo card with the answers, and calling cards with the shapes

Extra support and extra challenge with area and perimeter

For children who need more support: start with squares on a grid, and count them one by one. Color the inside for the area, and trace the outside edge in another color for the perimeter. Say the units aloud: square units for area, units for perimeter. Do the grid sheets before the sheets that use only side lengths, and use the answer key to check.

For children who need more challenge: ask for the rectangle with a perimeter of 30 and the greatest area, for an L-shape with an area of 30, and for two shapes with the same perimeter and different areas. The sheets with larger rectangles and the missing sides are good challenges, and so is the L-shape with a cut-out.

How to tell that a child is ready to move on from area and perimeter

Before moving on from area and perimeter, check that the child can do all four of these things:

1. The child counts squares to find the area of a shape on a grid.
2. The child finds the perimeter by adding all the sides.
3. The child uses length × width for the area of a rectangle.
4. The child finds a missing side from the area.

When all four are true, move on to the converting units page, or the measuring length page.

A 20-minute lesson on area and perimeter

A short lesson is the best way to introduce area and perimeter. This 20-minute plan can be used in a classroom, at a tutoring session or at home, and it uses the worksheets at the end:

Where area and perimeter fits across the grades

No skill stands alone. This table shows what children learn before and after area and perimeter, with the standard that goes with each step:

This page is the main page for area and perimeter. The whole sequence is on the measurement worksheets page.

Helping at home with area and perimeter

Parents do not need to be experts to help with area and perimeter. These suggestions work well, and each takes only a few minutes:

• Measure a room or a table and find its area and perimeter.
• Ask “how much fence?” or “how much carpet?” to see the difference.
• Use graph paper to draw a rectangle and count the squares.
• Use a baking tray to find the area of the cake.
• Check each answer for the right units.

How to check progress in area and perimeter

A teacher or parent can check progress in area and perimeter with the answer key and a few questions. This table shows three common situations, what they mean and what to do next:

A five-day plan for area and perimeter

Most children need about a week of short sessions for area and perimeter. This plan follows the order of the worksheets on this page:

When the plan for area and perimeter is complete, move on to the converting units page. The whole sequence is on the measurement worksheets page.