Area and Perimeter: What Is the Difference?
Area is how much surface a shape covers. On squared paper where each square is 1 cm by 1 cm, the area is the number of squares inside the shape, written in square centimetres, cm². Perimeter is the distance all the way round the outside of the shape. On the same grid, it is the number of square edges along the boundary, written in centimetres, cm. Area fills, perimeter fences.
One surprise worth showing your child in the shape lab: two shapes with the same area can have very different perimeters. Twelve squares in a 3 by 4 rectangle have a perimeter of 14 cm, but the same twelve squares in a long line of 1 by 12 have a perimeter of 26 cm. That is why the two measurements have to be worked out separately.
The Formulas
- Rectangle: area = length × breadth; perimeter = 2 × (length + breadth).
- Square: area = side × side; perimeter = 4 × side.
- Missing side from the area: breadth = area ÷ length. A rectangle with area 48 cm² and length 8 cm has breadth 6 cm.
- Missing side from the perimeter: halve the perimeter to get length + breadth, then take away the side you know.
- Triangle (P5): area = ½ × base × height, where the height is at right angles to the base. A triangle drawn inside a rectangle on the same base and with its top on the opposite side always has half the rectangle’s area.
How to Use This Page
- Pick the school year and an activity, then the number of questions, and press Start.
- Count on the grid: type the area and the perimeter of the coloured shape. A wrong answer shows each square numbered and the perimeter traced in red.
- Draw the shape: tap or drag across the grid to colour a shape that matches the task, for example an area of 12 cm² and a perimeter of 16 cm. There are many right answers; the page checks yours.
- Rectangles and squares: use the labelled sides to find the area, the perimeter or a missing side. The drawings are not to scale.
- L-shapes and shading: find the unlabelled sides, then the area or perimeter of the whole figure. In P5 this includes shaded triangles inside rectangles.
- Fix the ones you missed at the end of a round.
Activities by Level
| Level | What your child practises |
|---|---|
| P3 | Area by counting squares, perimeter by counting edges; drawing shapes with a given area; area and perimeter of rectangles and squares with sides up to 10 cm |
| P4 | Formulas for rectangles and squares; finding a missing side from the area or the perimeter; drawing a rectangle to a given area and perimeter; area and perimeter of L-shaped figures |
| P5 | All of P4, plus the area of a triangle (½ × base × height) and shaded triangles inside rectangles |
The levels follow the usual order in Singapore primary schools. Schools differ a little in pace, so move up or down freely.
Tips for Parents and Teachers
- Say the unit every time. Area answers end in cm² or m², perimeter answers in cm or m. Getting the unit right is often the clue that the right thing was worked out.
- Trace the perimeter with a finger. On L-shapes, children often miss the two short inner sides. Tracing the whole boundary and counting the sides catches it.
- Check an L-shape with its rectangle. The perimeter of an L-shape is the same as the perimeter of the rectangle around it. Its area is always smaller.
- Use real objects. Measure a table mat, a book or a floor tile and work out both. Square tiles on a floor are a ready-made grid.
- Keep it short. Five questions a day beats a long session once a week. The angles page and our worksheet generator cover the rest of P3–P5 geometry on screen and on paper.
Nothing to Install, Nothing Stored on Our Server
The practice runs entirely in your browser on any phone, tablet or computer. There is no account and no download. The last level and activity you chose are remembered on this device, and nothing about your child’s answers is sent to us.
Frequently Asked Questions
Area is the amount of surface a shape covers, measured in square units such as square centimetres (cm²). Perimeter is the distance all the way round the edge of a shape, measured in units of length such as centimetres (cm). A shape can have a large area and a small perimeter, or the other way round.
Area of a rectangle = length × breadth. Perimeter of a rectangle = length + breadth + length + breadth, or 2 × (length + breadth). For a square, area = side × side and perimeter = 4 × side.
Work out any unlabelled sides first, using the sides opposite them. Then add every side once, going all the way round. For an L-shape, the perimeter is the same as the perimeter of the rectangle that surrounds it, which is a useful check.
P3 finds area and perimeter by counting squares and edges, and works with simple rectangles and squares. P4 uses the formulas, finds a missing side from the area or perimeter, and adds L-shaped figures. P5 adds the area of a triangle and shaded triangles inside rectangles.
Yes. There is no account, no download and no limit on rounds. It works in any browser on a phone, tablet or computer, and nothing about your child’s answers is sent to us.