4th Grade Area and Perimeter of Rectangles Lesson: Notes and Examples (Free PDF)

4th grade area and perimeter lesson – Maths PDF

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This 4th grade area and perimeter lesson covers area and perimeter of rectangles (Common Core 4.MD.A.3), with a free PDF to print.

Key takeaway: This lesson helps fourth grade students find the area and perimeter of rectangles and squares and use those formulas to find a missing side.

Topic: Area and Perimeter of Rectangles (4th grade)
Content: One-page lesson with a definition, a worked example and key facts
Standards: 4.MD.A.3
Answers: Explanations included
Format: Free printable PDF, US Letter, black and white

Area is the number of unit squares that cover a flat shape, and perimeter is the distance around it. For a rectangle, area = length × width and perimeter = 2 × length + 2 × width. A rectangle 8 feet long and 3 feet wide has an area of 24 square feet and a perimeter of 22 feet.

This lesson helps fourth grade students find the area and perimeter of rectangles and squares and use those formulas to find a missing side. Also, it keeps the two ideas apart: area counts the flat space inside a shape, and perimeter measures the distance around it.

The lesson starts by counting unit squares, then builds the formula for area, then the formula for perimeter. Then, it finishes with problems that give the area or the perimeter and ask for a missing length or width. Also, each idea has a picture and a short example. Then, plan about 20 minutes, and sketch every rectangle on grid paper as you go.

Grade 4 · Common Core State Standards: 4.MD.A.3

Key facts in this 4th grade area and perimeter lesson

Key facts

Area of a rectangle = length × width, measured in square units.
Perimeter of a rectangle = 2 × length + 2 × width, measured in plain units.
A square is a rectangle whose four sides are equal.
Then, if you know the area and one side, divide to find the other side.
Area tells how much to cover; perimeter tells how far around.

What is the area of a rectangle?

Area tells how much flat space a shape covers. We count unit squares, like floor tiles. This rectangle has 6 squares in every row and 4 rows, so it has 24 squares.

6 columns and 4 rows of unit squares.

Area of a rectangle

\(A = l \times w\) where l is the length and w is the width. Area is measured in square units, such as square feet (sq ft) or square inches (sq in).

What is the perimeter of a rectangle?

Perimeter is the distance around the outside edge. Imagine walking along a fence. A rectangle has two long sides and two short sides, so add them all.

Walk around: 9 + 5 + 9 + 5.

Perimeter of a rectangle

\(P = 2 \times l + 2 \times w\) or \(P = 2 \times (l + w)\). Perimeter is measured in plain units, such as feet or inches.

How do you find a missing side of a rectangle?

Area is length times width, so use division to undo it. If a rectangle has an area of 48 square feet and a length of 8 feet, then the width is \(48 \div 8 = 6\) feet.

The area and one side are known.

How do you solve an area or perimeter word problem?

First decide what the question needs. A fence, a border, or a ribbon around something means perimeter. Carpet, paint, or grass covering something means area.

Example. Maya’s garden is 9 ft long and 5 ft wide. How much fence goes around it, and how much soil covers it?

Fence is around the edge, so find the perimeter: \(2 \times 9 + 2 \times 5 = 18 + 10 = 28\) ft.
Soil covers the garden, so find the area: \(9 \times 5 = 45\) square feet.
Write the units: 28 ft of fence and 45 sq ft of soil.

Pick the tool that fits the question.

4th grade area and perimeter lesson: questions and answers

What is the difference between area and perimeter?

Perimeter is the distance around a shape, so you add the side lengths. Area is the amount of space inside a shape, so you multiply length by width.

Why is area measured in square units?

Area counts squares that fit inside a shape. A square foot is a square that is 1 foot on each side, so the area of a floor is written in square feet.

How do you find the perimeter of a square?

A square has four equal sides, so multiply one side by 4. A square with sides of 6 inches has a perimeter of 4 × 6 = 24 inches.

How do you find a missing width when you know the perimeter?

Subtract the two known lengths from the perimeter, then divide by 2. If P = 30 in and the length is 9 in, then 30 – 18 = 12 and 12 ÷ 2 = 6 in.

Can two rectangles have the same perimeter but different areas?

Yes. A 7 ft by 3 ft rectangle and a 5 ft by 5 ft rectangle both have a perimeter of 20 ft, but their areas are 21 sq ft and 25 sq ft.

Common mistakes with this 4th grade area and perimeter lesson

Students write the answer to an area problem in feet instead of square feet. Area counts squares, so always write square units such as sq ft or sq in.
Students add only the length and width when finding perimeter. A rectangle has four sides, so double that sum or add all four sides.
Students multiply when they should add, because they mix up the two words. Instead, ask yourself whether you are covering a surface or walking around the edge.

How to study this chapter

Draw and label the rectangle before choosing a formula. A quick sketch shows which numbers are sides and which number is the answer.
Use a pair of memory hooks: area is the carpet inside a room, and perimeter is the baseboard around the walls.
Parents can measure a table or a rug at home with the child, then find both the area and the perimeter and talk about which one a store would need.

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