What is the difference between area and perimeter?

Perimeter is the distance around a shape, measured in units such as cm or m. Area is the space inside it, measured in square units such as cm² or m².

How do you find the area of a rectangle?

Multiply the length by the width. A rectangle 9 cm long and 6 cm wide has an area of 9 × 6 = 54 cm².

How do you find the perimeter of a rectangle?

Add all four sides, or double the sum of the length and width. A 9 cm by 6 cm rectangle has a perimeter of 2 × (9 + 6) = 30 cm.

How do you find a missing side of a rectangle?

From the area, divide the area by the side you know: 48 cm² with a side of 6 cm gives 8 cm. From the perimeter, halve it and subtract the side you know: a perimeter of 28 cm and a length of 9 cm give 14 − 9 = 5 cm.

Can two shapes have the same area but different perimeters?

Yes. A 2 cm by 8 cm rectangle and a 4 cm by 4 cm square both have an area of 16 cm², but their perimeters are 20 cm and 16 cm.

What grade learns area and perimeter?

In the US, grade 3 introduces both (3.MD.C and 3.MD.D), and grade 4 applies the rectangle formulas to real problems (4.MD.A.3). In England, perimeter starts in Year 3, area by counting squares in Year 4, and calculating the area of rectangles in Year 5.

Is there a free area and perimeter worksheet with answers?

Yes. Use the Print a worksheet button on this page. Each worksheet is freshly made, and the answer key can show answers only or answers with worked steps.

Grades 3 to 5 (Years 3 to 6 in England)

Area and perimeter of rectangles, with word problems

Here is how to find the area and perimeter of a rectangle, work back to a missing side and handle L-shapes, with a worked example and real-life word problems. Try the free practice below, then print a fresh area and perimeter worksheet with an answer key.

The method, step by step

Decide what the question wants: the distance around the edge (perimeter) or the space inside (area).
For perimeter, add all the side lengths; for a rectangle, 2 × (length + width) is a shortcut.
For the area of a rectangle, multiply the length by the width.
Write the units: centimeters (cm) for perimeter, square centimeters (cm²) for area.
Check that the answer is a sensible size for the shape.

CCSS 3.MD.C.5CCSS 3.MD.C.6CCSS 3.MD.C.7CCSS 3.MD.D.8CCSS 3.MD.C.7.BCCSS 4.MD.A.3England: Y4 MeasurementEngland: Y5 MeasurementEngland: Y3 MeasurementEngland: Y6 Measurement

Worked example

A rectangle is 8 cm long and 5 cm wide. Find its perimeter and its area.

Perimeter is the distance all the way around: 8 + 5 + 8 + 5.
8 + 5 + 8 + 5 = 26, so the perimeter is 26 cm.
Or use the shortcut: 2 × (8 + 5) = 2 × 13 = 26 cm.
Area is the number of 1 cm squares that cover the rectangle: 5 rows of 8 squares, or 8 × 5.
8 × 5 = 40, so the area is 40 cm².
Perimeter = 26 cm and area = 40 cm².

Practice now

Question 1 of 100 correct

A rectangle has a perimeter of 54 yd. Its length is 15 yd. What is its width, in yd?

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What area and perimeter mean

Perimeter is the distance around the outside of a shape. Imagine walking along the edge of a garden: the length of your walk is the perimeter, measured in units of length such as feet, meters or centimeters.

Area is the amount of flat space inside a shape, measured in squares. A square 1 cm on each side has an area of 1 square centimeter, written 1 cm². Cover a rectangle with these squares, with no gaps or overlaps, and the number of squares is its area.

Why area is length × width

A rectangle 6 cm long and 4 cm wide holds 4 rows of 1 cm squares, with 6 squares in each row. Counting them one by one gives 24, but multiplying is faster: 4 rows of 6 is 4 × 6 = 24 cm². That is why the area of a rectangle is length × width. It is the same array children meet when they learn their times tables.

A rectangle has two lengths and two widths, so its perimeter is length + width + length + width. The same 6 cm by 4 cm rectangle has a perimeter of 6 + 4 + 6 + 4 = 20 cm, which is also 2 × (6 + 4).

Area and perimeter examples

These examples get a little harder each time.

A square with sides of 9 m: the perimeter is 4 × 9 = 36 m and the area is 9 × 9 = 81 m².
A missing side from the area: a rectangle has an area of 42 cm² and one side of 7 cm. The other side is 42 ÷ 7 = 6 cm.
A missing side from the perimeter: a rectangle has a perimeter of 30 cm and a length of 9 cm. Length plus width is half of 30, which is 15, so the width is 15 − 9 = 6 cm.
The area of an L-shape: cut a 3 m by 2 m rectangle from the corner of a 10 m by 6 m rectangle. The area is 60 − 6 = 54 m².
The perimeter of the same L-shape: the two new edges, 3 m and 2 m, exactly replace the two pieces of edge that were cut away, so the perimeter is still 2 × (10 + 6) = 32 m.

An L-shape can also be split into two rectangles, with their areas added together. Both ways give the same answer, which makes a good check.

Area and perimeter word problems

The hardest part of a word problem is often choosing between area and perimeter. Fencing, a border, a frame, trim or a walk around the edge means perimeter. Carpet, paint, tiles, grass seed or anything that covers a surface means area.

Fencing a garden 12 m by 7 m takes 2 × (12 + 7) = 38 m of fence.
Carpeting a room 5 m by 4 m takes 5 × 4 = 20 m² of carpet.
A patio 6 m by 4 m, covered with square slabs 2 m by 2 m, fits 3 slabs along one side and 2 along the other, so it needs 3 × 2 = 6 slabs.
A poster has an area of 96 cm² and a width of 8 cm. Its length is 96 ÷ 8 = 12 cm, so its perimeter is 2 × (12 + 8) = 40 cm.

Same area, different perimeter

Two rectangles can have the same area but different perimeters. A 1 cm by 12 cm rectangle and a 3 cm by 4 cm rectangle both have an area of 12 cm², but their perimeters are 26 cm and 14 cm. Long, thin rectangles have the biggest perimeters for their area, and rectangles close to a square have the smallest.

How it is taught in school

In the US, Common Core introduces area in grade 3: measuring it by counting unit squares, connecting it to multiplication, and finding the area of shapes made from rectangles (3.MD.C.5 to 3.MD.C.7). Grade 3 also covers perimeter, including finding an unknown side and comparing rectangles with the same perimeter but different areas (3.MD.D.8). In grade 4, students apply the area and perimeter formulas for rectangles to real-world problems (4.MD.A.3).

In England, Year 3 pupils measure the perimeter of simple shapes. Year 4 pupils calculate the perimeter of rectilinear shapes and find area by counting squares. Year 5 pupils calculate and compare the area of rectangles in cm² and m², and Year 6 pupils learn that shapes with the same area can have different perimeters.

How parents can help

Measure a real room, table or garden together and work out both its area and its perimeter.
Use squared paper. Drawing rectangles and counting the squares shows why area is length × width.
Before each word problem, ask: is this about going around the edge or covering the inside?
Check the units every time. Perimeter is in cm or m; area is in cm² or m².
Keep sessions short. Print a fresh worksheet, let your child mark it with the answer key, and read the worked steps together for any they missed.

Common mistakes

Mixing up area and perimeter. For a 5 cm by 3 cm rectangle, the area is 15 cm² and the perimeter is 16 cm.
Adding only two sides for the perimeter. A 7 m by 4 m rectangle has a perimeter of 22 m, not 11 m.
Forgetting square units. Area is measured in squares, so write cm² or m², not cm or m.
Taking the length away from the whole perimeter to find the width. For a perimeter of 24 cm and a length of 8 cm, the width is 24 ÷ 2 − 8 = 4 cm, not 24 − 8 = 16 cm.
Using different units in one calculation. For a rectangle 2 m by 50 cm, change 2 m to 200 cm before multiplying.
Leaving out the short edges of an L-shape when finding its perimeter. An L-shape has six sides, so count them as you add.

Questions people ask

What is the difference between area and perimeter?: Perimeter is the distance around a shape, measured in units such as cm or m. Area is the space inside it, measured in square units such as cm² or m².
How do you find the area of a rectangle?: Multiply the length by the width. A rectangle 9 cm long and 6 cm wide has an area of 9 × 6 = 54 cm².
How do you find the perimeter of a rectangle?: Add all four sides, or double the sum of the length and width. A 9 cm by 6 cm rectangle has a perimeter of 2 × (9 + 6) = 30 cm.
How do you find a missing side of a rectangle?: From the area, divide the area by the side you know: 48 cm² with a side of 6 cm gives 8 cm. From the perimeter, halve it and subtract the side you know: a perimeter of 28 cm and a length of 9 cm give 14 − 9 = 5 cm.
Can two shapes have the same area but different perimeters?: Yes. A 2 cm by 8 cm rectangle and a 4 cm by 4 cm square both have an area of 16 cm², but their perimeters are 20 cm and 16 cm.
What grade learns area and perimeter?: In the US, grade 3 introduces both (3.MD.C and 3.MD.D), and grade 4 applies the rectangle formulas to real problems (4.MD.A.3). In England, perimeter starts in Year 3, area by counting squares in Year 4, and calculating the area of rectangles in Year 5.
Is there a free area and perimeter worksheet with answers?: Yes. Use the Print a worksheet button on this page. Each worksheet is freshly made, and the answer key can show answers only or answers with worked steps.

Updated November 1, 2026.

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