An L-shaped figure can have a smaller area than the rectangle it came from without having a smaller perimeter. This surprises many Primary 4 pupils because removing a corner seems as though it ought to shorten every measurement. For Serangoon North parents comparing weekday and weekend Mathematics tuition, this is a useful example of why perimeter demands careful tracing of the boundary rather than a quick subtraction of areas.
The learner needs to distinguish the length around the outside from the number of square units inside. For an L-shape made by removing a rectangular corner, the cut removes two pieces of the old boundary but introduces two new edges. Those changes must be traced, not guessed.
A good small-group tutorial lets the child sketch the shape, label lengths, calculate every boundary segment and check the result independently with new numbers. The right lesson day is one that leaves enough attention for careful geometric reasoning.
Find the next useful step
Starting-point check · Worked example · Weekday or weekend · Teaching and feedback · Independent review · Parent questions · Next step
Trace only the visible boundary before writing a formula
Draw a rectangle 10 cm wide and 7 cm high. From the upper-right corner, remove a smaller rectangle 4 cm wide and 3 cm high. The remaining figure is an L-shape with a rectangular corner missing.
Ask the child to shade the remaining L-shape lightly and trace its entire boundary with a finger. The outside of the remaining shape includes the edges newly exposed by the cut-out. It does not include the missing area itself.
Now label the lengths already known: the bottom remains 10 cm, the left side remains 7 cm, and the removed top-right rectangle measures 4 cm across and 3 cm down.
The right-hand exterior segment below the missing corner is 7 − 3 = 4 cm. The top horizontal segment left of the missing corner is 10 − 4 = 6 cm. The two inner edges of the L-shape are 4 cm and 3 cm because they are the sides of the removed corner.
Ask why the 4 cm horizontal segment in the notch must count as part of the perimeter. It is now a visible boundary of the remaining L-shape, even though it was not on the perimeter of the original full rectangle.
The first potential misconception is adding every number printed near the drawing, including dimensions that are not actual boundary segments. Let the child physically trace the path before deciding which lengths to add.
Calculate the perimeter of the L-shape without counting internal lines
Begin at the lower-left corner of the remaining L-shape and trace clockwise. The lengths encountered are: bottom 10 cm; right outer side below the notch 4 cm; horizontal inner notch 4 cm; vertical inner notch 3 cm; top remaining horizontal side 6 cm; and left outer side 7 cm.
Add the six boundary segments: 10 + 4 + 4 + 3 + 6 + 7 = 34 cm. The perimeter of the L-shape is 34 cm.
Check against the perimeter of the original 10 cm by 7 cm rectangle. That perimeter was 2 × (10 + 7) = 34 cm. In this specific kind of rectangular corner cut-out, the two old boundary pieces removed are exactly replaced in length by the two newly exposed inner edges.
This matching perimeter is not a rule for all notches and all shapes. A rectangular indentation cut from the middle of one side introduces extra boundary length, and an irregular cut-out may behave differently. Children should trace the actual remaining boundary rather than assume that every shape with a removed piece has unchanged perimeter.
For contrast, calculate the area if the child is ready: the original rectangle has area 10 × 7 = 70 cm². The removed corner has area 4 × 3 = 12 cm². The remaining area is 58 cm². These square centimetres measure surface, not perimeter. The perimeter remains 34 centimetres.
An error such as 34 − 4 − 3 = 27 cm ignores the two replacement edges. Show where the new horizontal and vertical boundaries appear. Another error is reporting 34 cm², which uses area units for a boundary length. The calculation may be right while the measured quantity is not.
Contents · Previous section · Next section
Choose a timetable that permits careful drawing and checking
A weekday lesson can help a Primary 4 pupil revisit a geometry problem immediately after it appears in school. An uncorrected sketch is especially useful evidence because a tutor can see whether an incorrect perimeter came from missing lengths, counting the wrong edges or confusing perimeter with area.
But geometry often requires more slow observation than a rushed end-of-day session permits. For Serangoon North families, consider the actual journey to the teaching venue, homework afterwards and whether the child will have enough attention to label each side rather than guess.
A weekend session may provide room to use graph paper, outline cut-outs and compare area with perimeter before writing a formal solution. The benefit depends on the child arriving with enough energy; a full weekend of activities can be just as tiring as a weekday evening.
Neither type of lesson should be judged only by how many shapes were completed. One L-shape drawn carefully, with every boundary segment explained, may show stronger understanding than several answers obtained by copying a formula.
Leave a new example for an independent revisit a few days later. When the child can draw, derive a missing side and check the perimeter without being prompted, the learning has begun to transfer beyond the tutorial.
Contents · Previous section · Next section
Use three-pupil discussion to separate drawing and arithmetic errors
In a 3-pax class, one learner might trace the entire visible boundary but forget to find the missing right-hand length. Another might know all lengths yet accidentally add one of them twice. A third might calculate the correct 34 but label it as square centimetres.
These require different responses. The first learner needs a clearer relationship between the original rectangle and the notch. The second may benefit from moving a finger around each segment once and marking it after it is counted. The third needs explicit distinction between length and area units.
Ask each pupil to explain what has happened to the two original corner boundary pieces. The top-right horizontal and upper-right vertical pieces disappeared, but edges of exactly the same lengths appeared along the indentation. This is the reason the perimeter is unchanged for this specific construction.
The tutor can ask the learner to verify the answer two ways: first by adding all six boundary segments and then by comparing the two removed lengths with their replacements. This is not a shortcut to memorise blindly; it is a structural check based on the figure.
For a linked discussion of measurement meanings, see Primary 4 Bukit Timah Mathematics Tuition: Area or Perimeter?. The eduKate Mathematics learning hub connects geometry with wider Primary Mathematics problem-solving skills.
Contents · Previous section · Next section
Review a 12 cm by 8 cm rectangle with a different corner removed
On another day, draw a new rectangle 12 cm wide and 8 cm high. Remove a rectangular corner 3 cm wide and 2 cm high from its upper-right corner. Ask the child for the remaining perimeter without showing the first L-shape.
Trace clockwise from the bottom-left corner. The bottom edge is 12 cm. The right-hand outer side below the notch is 8 − 2 = 6 cm. The inner horizontal edge is 3 cm and the inner vertical edge is 2 cm.
The remaining top horizontal edge is 12 − 3 = 9 cm, and the full left side is 8 cm. Thus the perimeter is 12 + 6 + 3 + 2 + 9 + 8 = 40 cm.
Check the original rectangle: 2 × (12 + 8) = 40 cm. The remaining L-shape has the same perimeter because the corner cut removed boundary pieces of lengths three and two and replaced them with new edges of lengths three and two.
Ask the learner whether the area also stayed the same. It did not. The original area was 96 cm², and the 3 cm by 2 cm removed corner had area 6 cm², leaving 90 cm². This reinforces that area and perimeter measure different things.
Preserve the first sketch, the labels and any corrections. A child who can identify all six boundary edges and justify both the numerical result and the units is showing transferable geometric reasoning, not merely repeating “two times length plus width” on every picture.
Contents · Previous section · Next section
Frequently asked questions from Serangoon North parents
Why does removing a rectangular corner not change this L-shape perimeter?
The two outer pieces removed from the boundary are replaced by inner edges of equal total length. This is specific to a rectangular corner cut and is not a rule for every possible indentation.
Why does the area change while the perimeter stays the same?
Area counts the surface inside the figure and loses the removed rectangular region. Perimeter measures the boundary length; here the replacement edges exactly compensate for the removed edges.
How should we choose between weekday and weekend tuition for geometry?
Choose a slot when the child can draw, label, trace and independently check a new figure. Travel, rest and the tutor’s response to the specific misconception matter more than the calendar label.
Contents · Previous section · Next section
Decide on the learning support and confirm the actual class
Bring a recent piece of Mathematics working and preserve the child’s first independent answer, including where an adult or tutor first intervened. The eduKate Mathematics learning hub and Singapore Mathematics tuition by area index provide broader routes, but this single question is only an initial diagnostic rather than a complete syllabus checklist.
Serangoon North identifies the families addressed here; it does not establish that eduKate operates a tuition centre at a specific Serangoon North address. Confirm the actual teaching venue, three-pupil class fit, travel, current availability, fees and the suitability of the weekday or weekend schedule directly. For a separate family-oriented local context, see Things to Do for Kids: Learning Serangoon North.
For a parent–student consultation with eduKate Singapore, share your child’s current level, one independent problem, the first help needed and a realistic weekly schedule. Ask what a fresh review task will look like after the tutorial; progress is better demonstrated by independent understanding than by copying a finished page.
Continue through Serangoon North Mathematics: Primary 1: Number Foundations · Primary 2: Core Numeracy · Primary 3: Problem-Solving · Primary 5: Cube Volume · Primary 6: Speed and Time · PSLE: Reverse Fractions · Exam Preparation: Containers. Explore the eduKate Mathematics Learning Hub for wider topic connections.