Primary Maths Area and Perimeter: Trace the Boundary of a Composite Shape

Start with what the question is measuring

A public SGExams discussion about difficult P5–P6 maths topics raised geometry and mensuration among the areas worth discussing. That is a useful starting point for a practical lesson: a child can remember the rectangle formulas yet still be unsure which lines belong in a composite shape's perimeter. The discussion is anecdotal, rather than evidence that one topic is hardest for every pupil.

MOE's Primary Mathematics syllabus, updated October 2025 includes finding the area and perimeter of composite figures made from rectangles and squares in Primary Four. The activity below revisits that foundation. All its dimensions and answers are original teaching examples.

Draw one shape and ask two different questions

On squared paper, draw a rectangle 10 cm wide and 6 cm tall. Remove a rectangle 4 cm wide and 2 cm tall from the top-right corner. The remaining shape looks like an L. Label the original bottom edge 10 cm and the original left edge 6 cm. Label the horizontal notch 4 cm and the vertical notch 2 cm.

Ask your child to shade the remaining paper. That shaded region is what an area question measures. Then ask them to move a pencil around its complete outside boundary, including the two edges of the notch. That journey is what a perimeter question measures. A line drawn inside the shape to help with a calculation is different: it is not part of the outside boundary.

Find area in two ways

The full rectangle has area 10 × 6 = 60 cm². The removed corner has area 4 × 2 = 8 cm². Therefore the L-shaped region has area 60 − 8 = 52 cm². Ask your child to point to the region represented by each multiplication before writing the subtraction.

For a second method, split the L horizontally at the bottom of the notch. The lower rectangle is 10 cm by 4 cm, because 6 − 2 = 4. The upper-left rectangle is 6 cm by 2 cm, because 10 − 4 = 6. Their areas are 40 cm² and 12 cm². Adding gives the same 52 cm². Checking by another split is useful because it tests whether the chosen rectangles actually cover the region without gaps or overlap.

Walk around every exposed edge

Starting at the bottom-left corner and moving along the bottom, the six boundary lengths are 10, 4, 4, 2, 6 and 6 cm. Their sum is 32 cm. Let your child mark a small tick on each edge after counting it. This makes a missed notch or a repeated edge easier to spot.

The original rectangle also had perimeter 2 × (10 + 6) = 32 cm. Here the corner cut removed an outer horizontal length of 4 cm and an outer vertical length of 2 cm, but introduced notch edges of exactly those lengths. The area decreased while the perimeter stayed the same. This conclusion belongs to this corner-cut arrangement; it is not a rule that every cut leaves perimeter unchanged.

Use a comparison to test understanding

Draw a second 10 cm by 6 cm rectangle. This time remove a rectangular notch 4 cm wide and 2 cm deep from the middle of its top edge, without reaching either side. Its area is again 52 cm². Its perimeter is now 36 cm: the 4 cm horizontal opening is replaced by another 4 cm horizontal edge, while two extra vertical edges of 2 cm are added. Your child should trace those extra edges rather than memorise an adjustment rule.

Choose a small amount of follow-up practice

Use the TestPapersFree Primary Maths collection to select a few rectangle-and-square composite questions at your child's level. Before calculating, have them label missing sides, shade the required region and trace its boundary. After checking, record whether an error came from a missing length, an internal dividing line, arithmetic or units. Area needs square units; perimeter needs length units. Revisit the specific mistake with one changed diagram before moving to a full paper.