This grade 3 area lesson explains area in one printable page, with definitions, a method and a worked example.
Area is the amount of flat space inside a shape. We measure it by counting unit squares, which are squares with sides 1 unit long. The area of a rectangle equals its rows times its columns, so a rectangle 5 units wide and 3 units tall has an area of 15 square units.
Grade 3 Area Lesson: key facts
- A unit square has sides 1 unit long and an area of 1 square unit.
- Area is measured in square units such as sq cm, sq in, sq ft and sq m.
- Area of a rectangle = length times width, which is rows times columns.
- A rectangle can be split into parts, and the whole area is the sum of the part areas.
- To find the area of an L-shape, split it into rectangles and add their areas.
What is area?
Area is the amount of flat space inside a shape. To measure it, cover the shape with unit squares that fit together with no gaps and no overlaps. A unit square has sides 1 unit long, and it covers 1 square unit. Count the squares and you know the area.
Area is written in square units: square centimeters (sq cm), square inches (sq in), square feet (sq ft) or square meters (sq m). The word square tells us we are counting squares, not lengths.
How do you find the area of a rectangle by multiplying?
Rows of squares make an array. A rectangle with 4 rows and 6 squares in each row has \(4 \times 6 = 24\) squares. So you can skip the counting and multiply the two side lengths.
| Length | Width | Area |
|---|---|---|
| 3 ft | 2 ft | \(3 \times 2 = 6\) sq ft |
| 5 ft | 4 ft | \(5 \times 4 = 20\) sq ft |
| 6 ft | 3 ft | \(6 \times 3 = 18\) sq ft |
How does the distributive property help with area?
Big rectangles can be split into smaller ones. A rectangle 7 units wide and 6 units tall can be cut into a part 5 wide and a part 2 wide. Find each part, then add: \(6 \times 7 = 6 \times (5 + 2) = 30 + 12 = 42\). Splitting one side into two parts is the distributive property.
How do you find the area of an L-shaped figure?
An L-shape is not a rectangle, but it is made of rectangles. Split it, find each area, and add the areas.
- Draw a line that cuts the figure into two rectangles.
- Find the length and width of each rectangle. Use the outside numbers: the tall side is 6 units, and the top bar is 2 units tall, so the lower part is \(6 – 2 = 4\) units tall.
- Multiply for each rectangle: \(8 \times 2 = 16\) and \(3 \times 4 = 12\).
- Add: \(16 + 12 = 28\) square units.
Can different rectangles have the same area?
Yes. A 2-by-6, a 3-by-4 and a 1-by-12 rectangle all have an area of 12 square units, because \(2 \times 6 = 3 \times 4 = 1 \times 12 = 12\). The shapes look different, but they cover the same amount of flat space.
Area: frequently asked questions
What is a square unit?
A square unit is a square whose sides are all 1 unit long, such as 1 centimeter or 1 foot. It covers exactly 1 square unit of area. We count square units to measure how much flat space a shape covers.
Why is area written in square units?
Area counts squares that cover a shape, not lengths along its edge. A rectangle that is 4 feet by 3 feet is covered by 12 squares that are each 1 foot on a side, so its area is 12 square feet.
How do you find a missing side when you know the area?
Think of a multiplication fact with a missing factor. If a rectangle has an area of 35 square inches and a length of 7 inches, ask what number times 7 makes 35. The width is 5 inches.
What is the distributive property in an area model?
It means you can split one side of a rectangle into two parts and add the two smaller areas. For example, 6 times 8 equals 6 times 5 plus 6 times 3, which is 30 plus 18, or 48.
Does turning a rectangle change its area?
No. A rectangle that is 3 units wide and 5 units tall covers the same 15 square units as one that is 5 units wide and 3 units tall. Turning or sliding a shape never changes its area.
How to use this grade 3 area lesson
Use this grade 3 area lesson before the worksheet, then check what you learned with the quiz.
See every chapter on the Grade 3 math page.
