A rectangular poster measures 12 cm by 9 cm. A 5 cm by 4 cm rectangular corner is removed from its upper-right side, producing an L-shape. What is the remaining area? The answer is 88 cm². For Serangoon North Avenue 3 parents comparing weekday and weekend Primary 4 Mathematics tuition, this problem reveals whether a child can see a composite figure as the difference or sum of rectangles.
The same drawing raises a second question: what is the perimeter of the remaining L-shape? For this specific corner cut-out, the perimeter is 42 cm, equal to that of the original 12 cm by 9 cm rectangle. The area decreased, but the newly exposed edges replace the removed outer edge lengths.
Singapore’s Primary 4 Mathematics syllabus includes finding the area and perimeter of composite figures made from rectangles and squares. A good tutorial should distinguish surface area, outside boundary and missing dimensions, then test the reasoning on a new diagram instead of memorising one L-shape answer.
Find the next useful step
The question and its answer · See the starting-point misconception · Build the mathematical model · Complete the worked example · Use a second method to verify · Diagnose typical errors · Choose a weekday lesson · Choose a weekend lesson · How three-pupil feedback improves the lesson · Four-week evidence plan · Independent transfer problem · Questions parents ask · Consultation and next steps
The remaining area is 88 cm², with a 42 cm boundary
The original rectangle has area 12 × 9 = 108 cm². The removed upper-right rectangular corner has area 5 × 4 = 20 cm².
Subtract the missing surface: 108 − 20 = 88 cm². The L-shape contains eighty-eight square centimetres of area.
Its perimeter is found by adding the remaining outside edges, including the two new edges exposed by removing the corner. Their lengths are 12, 5, 5, 4, 7 and 9 centimetres in order around the figure.
The sum is 12 + 5 + 5 + 4 + 7 + 9 = 42 cm. The answer is a length, not an area, so it uses centimetres rather than square centimetres.
A useful immediate check is that 88 cm² must be smaller than the original 108 cm² because some surface was removed. The result cannot be larger than the starting poster in this story.
The fact that the perimeter is unchanged applies to this rectangular cut from an outside corner. It should not be turned into a rule that every notch or removed region leaves perimeter unchanged.
A well-taught pupil explains why the area and perimeter behave differently rather than accepting two unrelated formulas.
Identify the original rectangle, removed corner and remaining L-shape
Draw a horizontal rectangle with width 12 cm and height 9 cm. Mark its upper-right corner and draw a smaller rectangular region 5 cm wide along the top edge and 4 cm tall down the right edge.
Shade the remaining L-shaped region and leave the upper-right 5 cm by 4 cm corner unshaded. The shaded part should be connected, extending the full twelve centimetres across the bottom and nine centimetres up the left.
The outer boundary of the original complete rectangle is not the same as the outer boundary of the remaining L. Two original corner-edge pieces are missing, and two new interior-facing edges become part of the L’s outside boundary.
Ask the child which lengths are given, and which must be calculated. The bottom remains 12 cm and left side remains 9 cm. The top remaining horizontal segment is 12 − 5 = 7 cm.
The right lower vertical segment is 9 − 4 = 5 cm. The new horizontal notch edge is 5 cm and the new vertical notch edge is 4 cm, matching the dimensions of the removed rectangle.
Trace the whole boundary slowly with a finger, beginning at the lower-left corner and returning to it. The trace should touch each of the six boundary segments exactly once.
A pupil who counts only the original outer portions will miss the notch edges. Another who includes the old top-right corner lines that have been removed will overcount. The drawing is the key diagnostic.
The tutor should preserve the learner’s first marked sketch and note where the boundary or missing-dimension interpretation became uncertain.
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Find the area by subtracting the missing rectangular part
The area of the complete 12 cm by 9 cm rectangle is 12 × 9 = 108 cm². This is the full surface before the corner is cut away.
The cut-out rectangle is 5 cm by 4 cm, so its area is 5 × 4 = 20 cm². It is missing from the final figure.
The remaining area is therefore 108 − 20 = 88 cm². The operation matches the story: a whole surface has lost one non-overlapping rectangular section.
Ask why the unit is cm². Area counts the number of 1 cm by 1 cm squares needed to cover a region, not the distance traced around the outer edge.
An estimate can show that the answer should be somewhat below one hundred square centimetres but above half of the original 108. The removed corner is relatively small compared with the full rectangle.
A learner who writes 108 + 20 = 128 has added the removed part rather than subtracting it. Ask whether cutting a piece away can make the remaining shaded area larger in this construction.
Another learner may compute 12 + 9 − 5 − 4 and label the result as area. This uses side lengths without multiplying to measure the surface; return to rectangle arrays or the familiar area formula.
The subtraction method is especially efficient when the original rectangle and the cut-out dimensions are all known. It is not the only valid method, and a second construction can verify it.
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Verify the area by splitting the L into two non-overlapping rectangles
Instead of subtracting from the full surface, divide the remaining L into two rectangles that do not overlap.
The entire left strip is 7 cm wide and 9 cm high. Its area is 7 × 9 = 63 cm².
The bottom-right strip is 5 cm wide and 5 cm high, because the remaining right vertical height is 9 − 4 = 5. Its area is 5 × 5 = 25 cm².
The two pieces fit together exactly without gaps or overlap. Adding their areas gives 63 + 25 = 88 cm².
This matches the subtraction method. Two different decompositions therefore confirm the same total surface, giving the learner a way to spot arithmetic or interpretation mistakes.
An incorrect decomposition would use a 7 × 9 left strip and a 12 × 5 bottom strip, which overlap over part of the L. Adding their full areas would count that overlap twice.
Ask the child to point to the boundary separating the two rectangles and show that every shaded portion belongs to exactly one of them.
A good tutor can choose either decomposition depending on the learner’s drawing, but should explain why the chosen pieces represent the whole once and only once.
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Calculate the perimeter from six outside edges
Start at the lower-left corner and move clockwise around the L-shape. The bottom horizontal edge is 12 cm; the right lower vertical edge is 5 cm.
Next trace the inward horizontal notch edge of 5 cm, then the upward vertical notch edge of 4 cm. Both are on the new outside boundary because the removed corner is empty.
Continue along the remaining top horizontal edge of 7 cm, then down the full left side of 9 cm to return to the starting point.
The full perimeter is 12 + 5 + 5 + 4 + 7 + 9 = 42 cm. A perimeter is a length, so use cm rather than cm².
Compare this with the original rectangle’s perimeter: 2 × (12 + 9) = 42 cm. The two removed outside edge portions were 5 cm and 4 cm, together nine centimetres.
Those removed portions were replaced along the notch by two new exposed edges of the same lengths, also totalling nine centimetres. The net change in the boundary length is zero.
The perimeter is unchanged for this particular corner cut, even though the area has decreased by twenty square centimetres.
An indentation cut from the middle of a side can introduce extra boundary length; the child should not generalise the equal-perimeter result beyond the geometry actually drawn.
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Use the first mistake to choose the next lesson
If the learner writes 108 cm² for the L-shape, they have calculated the original rectangle but overlooked the removed corner. Ask which region is no longer part of the final figure.
If the answer is 128 cm², the learner likely added the cut-out instead of subtracting it. Ask whether the finished shape has more or less surface than the starting poster.
If a student obtains 88 but labels it cm, the area calculation may be sound while the unit meaning is not. Explain the difference between measuring surface squares and tracing boundary length.
A perimeter answer of 33 cm suggests the new notch edges may have been omitted. Trace the six exposed segments and point to the 5 cm and 4 cm interior-facing boundaries.
An answer of 51 cm may arise from adding an edge twice or including part of the boundary that was removed. Have the pupil mark each segment after it is counted.
If a pupil splits the shape into overlapping rectangles and gets more than 108 cm², the decomposition is invalid. Compare the shaded portions and find the overlap.
A tutor who knows the first wrong step can target area interpretation, missing lengths, units or arithmetic individually instead of assigning a generic set of geometry worksheets.
Retaining the first diagram is important; it can show what a pupil thought the figure consisted of before the teacher provided the correct boundary.
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A weekday lesson can focus on a recent composite-figure error
A weekday Primary 4 Mathematics tutorial may fit when the pupil has just encountered a composite area question in school. The uncorrected drawing can show whether the difficulty began with the cut-out, the missing side length or the unit.
Serangoon North Avenue 3 parents should confirm the real tuition venue and full door-to-door journey. A local article does not establish a branch in the nearby residential blocks.
Geometry benefits from careful drawing, annotation and self-checking. An overtired child may forget one boundary edge even when the underlying rule is understood at a calmer time.
A focused session can compare subtraction and non-overlapping addition methods for area, then trace the perimeter and review the different units.
If the weekday journey leaves too little room for food or recovery, consider a different hour rather than responding only with longer worksheets.
The later independent review should change both the rectangle dimensions and the size of the corner removed, preventing the child from relying on a memorised answer.
A sustainable tutorial complements schoolwork and rest instead of displacing them.
| Decision factor | Weekday tutorial | Weekend tutorial |
|---|---|---|
| Fresh schoolwork | Can correct a recent missing-edge or cut-out error while it is familiar | May permit physical cut-outs and a slower boundary explanation |
| Attention and commute | Check real venue, dismissal, meals and homework | Check family, sport and enrichment commitments |
| Evidence after tuition | Different composite figure a few days later | Unfamiliar L-shape during the following school week |
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A weekend session may provide more room for physical cut-outs
A weekend class may allow the tutor to use a rectangular card and cut out an upper-right corner, then let pupils trace the exposed perimeter with string or a finger.
The model can show that the surface area shrinks while two new boundary segments appear. This is particularly useful when a learner wrongly believes that a smaller shape must always have a shorter perimeter.
Ask each pupil to predict the new area and perimeter before the cut-out is removed, then verify using a labelled drawing. Prediction followed by explanation gives more insight than watching the tutor manipulate all materials.
Weekends may also be full of family activities, sports or other tuition. Compare the child’s actual attention to a possible settled weekday window.
After the physical demonstration, remove the model and ask the child to calculate a different L-shape on paper. The method should eventually be usable without tracing physical card every time.
A short follow-up on another day confirms whether the boundary-counting habit remains available when the familiar tutor is absent.
The goal is to build geometric reasoning rather than fill a longer session with decorative shape-cutting.
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Three pupils may each need a different geometry intervention
One pupil may choose subtraction correctly but calculate the cut-out area inaccurately. Another may find 88 cm² but omit notch edges in the perimeter. A third may add overlapping component rectangles and overcount surface.
The first needs multiplication or subtraction fluency. The second needs a boundary trace. The third needs a partition that accounts for every surface point exactly once.
Each learner should submit a first labelled diagram before hearing the answer. In a true 3-pax tutorial, the tutor can observe independent reasoning within the shared task.
A helpful prompt might be “Which part is missing?” for one student, “Where is the new boundary?” for another, and “Have you counted this shaded region twice?” for the third.
Parents should ask what the learner managed independently and which smaller prompt repaired the mistake. A correct final number copied from another pupil is not the same achievement.
The Primary 4 Mathematics study guide and area-versus-perimeter comparison provide wider routes, supported by the Mathematics learning hub.
The final aim is that each pupil can explain both a valid decomposition and the complete boundary without relying on the tutor’s specific diagram.
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Use four checkpoints to move from models to independent work
In week one, identify the outer rectangle, cut-out and six boundary segments. Ask the child to annotate an uncorrected L-shape independently.
Week two can teach two non-overlapping ways to find the same area: subtraction from a whole, and addition of component rectangles. Both should agree.
Week three can compare area and perimeter on a few different composite figures, including a deliberate counterexample to the idea that every removed region leaves perimeter unchanged.
Week four can use an unfamiliar L-shape after a gap. The learner should identify missing side lengths, calculate both quantities and check the answers without adult prompts.
Record the first diagram, original computation, smallest helpful hint and later independent attempt. This is more useful than measuring progress through worksheet volume alone.
If a pupil understands area but struggles with boundary tracing, keep perimeter work separate until it is secure. If missing side lengths are the primary gap, practise subtraction of dimensions before returning to the full figure.
These weeks are illustrative checkpoints, not a guaranteed mastery deadline. Use the child’s current schoolwork and readiness to select the next task.
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Independent transfer: a 15 cm by 10 cm poster with a 6 cm by 3 cm corner removed
On another day, draw a new 15 cm by 10 cm rectangle with a 6 cm by 3 cm rectangular corner removed from the upper right. Ask the child to calculate the remaining area and perimeter before seeing the original 12-by-9 example.
The full rectangle has area 15 × 10 = 150 cm². The removed section has area 6 × 3 = 18 cm².
The remaining area is 150 − 18 = 132 cm². As another check, the left strip is 9 × 10 = 90 cm², and the bottom-right strip is 6 × 7 = 42 cm². Their sum is 132 cm².
For perimeter, trace the bottom 15 cm, right lower edge 7 cm, inner horizontal edge 6 cm, inner vertical edge 3 cm, top remaining edge 9 cm and left outer edge 10 cm.
Their sum is 15 + 7 + 6 + 3 + 9 + 10 = 50 cm. This matches the perimeter of the original rectangle, 2 × (15 + 10) = 50 cm, for the same corner-replacement reason.
Ask what would happen if the 6-by-3 rectangle were removed from the middle of the top edge instead of the upper-right corner. The remaining boundary would require a different trace; the perimeter need not remain fifty.
Record the first independent diagram and any hints given. A pupil who obtains both 132 cm² and 50 cm, verifies the two decompositions and explains the boundary replacement has transferred the reasoning to new dimensions.
The final answer must preserve units: cm² for area and cm for perimeter. They measure different properties even when calculated from the same picture.
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Questions Serangoon North Avenue 3 parents ask
What is the area after removing a 5 cm by 4 cm corner from a 12 cm by 9 cm rectangle?
The original area is 108 cm² and the removed region is 20 cm², so 88 cm² remains.
Why is the perimeter still 42 cm?
The removed outer boundary lengths of five and four centimetres are replaced by newly exposed notch edges of the same lengths. That equality applies to this rectangular corner cut.
Can perimeter stay the same even when area decreases?
Yes, as this corner-removal example demonstrates. Different removals or indentations can change perimeter in other ways.
What makes a valid area decomposition?
The chosen rectangles must cover every part of the remaining figure without gaps or overlaps. Here 63 cm² and 25 cm² add to 88 cm².
Which tuition day should a child choose for composite geometry?
Choose the slot where the pupil can draw, label, compute and check a new figure attentively, with realistic travel and rest.
Plan the tutorial around the earliest unstable step
The MOE Primary Mathematics syllabus, updated October 2025, is the official reference for curriculum progression. The eduKate Mathematics learning hub and Singapore Mathematics tuition by area index provide wider routes. This page explores one well-defined skill with an example; it is not a complete syllabus assessment or a guaranteed improvement timetable.
Serangoon North Avenue 3 identifies the families addressed by this guide, not the address of a claimed new eduKate branch. Confirm the actual teaching location, fees, currently available session times, a genuine three-pupil group fit and the child’s door-to-door journey. Read Learning Serangoon North for separate neighbourhood context; the location of a family resource does not establish a tuition venue.
Bring the student’s original, uncorrected work and an explanation of the first hint that was needed. For a parent–student consultation, ask how the tutor will move from that starting point towards a delayed, independent example with different numbers. A sustainable timetable protects schoolwork, food, rest and family commitments as well as instructional time.
Continue through the Serangoon North Avenue 3 Mathematics guides
Follow a different Primary level for another syllabus-aligned Mathematics example and an independently checked weekday-versus-weekend tuition decision. Each page focuses on a different learning gap.
- Primary 1: Two-digit addition and place value
- Primary 2: Repeating patterns with colour and shape
- Primary 3: Reading bar graphs with a scale of five
For a different worked example at the same level, see Primary 4 Mathematics Tuition | Serangoon North Avenue 2. The eduKate Mathematics learning hub connects the wider curriculum.
Continue through Serangoon North Avenue 3 Mathematics: Primary 5: Two-Tank Volume · Primary 6: Equal-Addition Ratios · PSLE: Two-Price Ticket Reasoning · Exam Prep: Timetable Checks. These guides develop different level-specific mathematical skills.