Secondary 1 G1 Mathematics Tutor Bukit Timah. Did you know? Cutting a rectangle’s corner may change its area without changing its perimeter. Learn to trace L-shaped boundaries. A fast-reading guide with a useful “Did you know?” insight, everyday examples, a common misconception and a short home check.
Start with the explanation that changes the first decision. Then ask your child to solve a changed example independently. Understanding is more valuable than copying a finished line.
Jump to: Quick insight · Five-minute practice · Frequently asked questions.
Did you know? Cutting off a corner may leave the perimeter unchanged
Did you know? A rectangle can lose a small rectangular corner, becoming L-shaped, yet have exactly the same perimeter as before. Its area becomes smaller, but the distance around the outside can stay the same.
That sounds surprising until you trace every boundary segment. In Secondary 1 G1 Mathematics, perimeter questions are often lost because a pupil adds only the lengths printed on a diagram or includes a line that is not part of the outside boundary.
The key is to separate two questions: What area remains inside? and What is the complete path around the outside? They are not the same operation.
Start with a simple rectangle
Imagine a fictional cardboard rectangle measuring 8 cm by 6 cm. Its perimeter is 8 + 6 + 8 + 6 = 28 cm. Its area is 8 × 6 = 48 cm².
Trace the boundary in order: eight centimetres along the bottom, six up the right side, eight along the top and six down the left side. Return to the starting point. Perimeter is a complete journey around a closed shape.
Area, by contrast, measures the two-dimensional region inside the boundary. The different units help remind us that the questions are measuring different things.
Now remove a 3 cm by 2 cm corner
Suppose we cut a 3 cm-wide and 2 cm-deep rectangular piece from the top-right corner of the 8 cm by 6 cm rectangle. The remaining cardboard is L-shaped. Its area is the original 48 cm² minus 3 × 2 = 6 cm², so 42 cm² remains.
To calculate its perimeter, do not simply subtract the old corner edges. The 3 cm of top edge and 2 cm of right edge that disappear are replaced by a new horizontal boundary of 3 cm and a new vertical boundary of 2 cm.
The total perimeter therefore remains 28 cm. The boundary has taken a detour but the cut-off lengths have been replaced by equal lengths inside the notch.
Find the hidden horizontal and vertical lengths
After the corner is removed, the top outer edge measures 8 − 3 = 5 cm. The right outer edge below the cut measures 6 − 2 = 4 cm. The two new inner step edges measure 3 cm horizontally and 2 cm vertically.
Trace all six edges in sequence: bottom 8 cm, right outer side 4 cm, notch horizontal 3 cm, notch vertical 2 cm, top outer side 5 cm and left outer side 6 cm.
Adding them gives 8 + 4 + 3 + 2 + 5 + 6 = 28 cm. This method is dependable because it checks every outside segment rather than assuming the perimeter formula for a rectangle still applies.
Note that the ‘same perimeter’ result is a helpful shortcut for this particular corner-cut construction. It is not a universal rule for every L-shaped or indented figure.
An indentation in the middle behaves differently
Now take another 8 cm by 6 cm rectangle and cut a 3 cm-wide, 2 cm-deep notch down from the middle of its top edge, without reaching either corner. The removed area is still 6 cm², so the remaining area is again 42 cm².
But the perimeter increases. The notch replaces a 3 cm section of the former top edge with three segments: down 2 cm, across 3 cm and up 2 cm. Those total 7 cm. We removed 3 cm of old boundary and added 7 cm, a net increase of 4 cm.
The new perimeter is 28 + 4 = 32 cm. This shows why two shapes of the same area can have different perimeters. Where the material is removed matters.
A reliable routine for missing edges
First mark the complete outer width and height of the figure. Next find missing horizontal lengths by subtracting labelled horizontal parts from the total width; do the same vertically. Write the found lengths directly beside the appropriate edges.
Then choose one starting point and trace the boundary clockwise. Include each outside segment exactly once. Do not jump across an empty cut-out, count a line inside the shape, or ignore the short edges of the notch.
Finally, check the unit: a perimeter is a length, so the answer should use cm, m or another length unit. If you calculate an area as a separate check, use cm² or m². The labels help tell you whether the two quantities have accidentally been mixed.
What changes when an L-shape is rotated?
Nothing about its lengths, area or perimeter changes when the diagram is turned on the page. A notch drawn at the bottom-left still creates new boundary edges that must be counted. A problem that looks different may represent exactly the same shape.
Ask your child to rotate the paper and explain why the boundary length does not change. This reveals whether they are interpreting the geometric relationships or depending on the drawing being oriented a particular way.
That is an important form of mathematical confidence: a different-looking figure does not automatically demand a different rule.
Why small-group feedback is useful
One student may calculate the area correctly but forget the inner notch edges when finding perimeter. Another may include the removed corner’s old edges and count the new edges as well. A third may calculate the missing lengths correctly but add an internal line that is not part of the boundary.
eduKateSG’s published Secondary 1 Mathematics small-group programme near Sixth Avenue MRT uses three-pupil tutorials of 1.5 hours weekly. A tutor can follow each pupil’s pencil around a diagram, ask them to explain what they counted and then give a rotated L-shape to test whether the understanding holds.
For a parent, the most useful question is often “Which edge did you miss or count twice?” rather than “Why did you not remember the formula?”
Five-minute L-shape practice
A. A rectangle measures 8 cm by 6 cm. Find its perimeter and area. Answer: 28 cm and 48 cm².
B. Cut a 3 cm by 2 cm rectangular corner from it. Find the new perimeter and area. Answer: 28 cm and 42 cm².
C. Instead, cut a 3 cm-wide, 2 cm-deep notch from the middle of the top edge. Find the new perimeter and area. Answer: 32 cm and 42 cm².
Ask the learner to sketch both cut-out shapes and trace the outside with a finger. The different perimeters should make sense from the boundary, not just from the final arithmetic.
Frequently asked questions
Does every L-shape have the same perimeter as its outer rectangle? No. The special equality shown here holds for the specified rectangular corner cut; other indentations can increase perimeter.
Are perimeter and area of composite figures part of Secondary 1 G1 Maths? Yes. Mensuration and problems involving perimeter and area of plane figures are part of the G1 geometry and measurement foundations.
Why does the final unit matter? Perimeter measures distance around the edge, while area measures the surface inside the figure.
Continue learning: Secondary 1 G1 Mathematics guides
- Fractions Between Zero and One: Comparing Sizes
- Algebraic Fraction Bars: The Hidden Brackets
- Triangle Angles: Why They Add to 180 Degrees
- Why Area and Perimeter Differ
- Parallelogram and Trapezium Area
To understand eduKateSG’s established learning approach, read the original Secondary 1 Mathematics small-group tutorials guide. This original reference is unchanged. Its published programme describes three-student tutorials near Sixth Avenue MRT, with 1.5-hour weekly lessons and guided corrections.
For the subject-level scope, consult the Ministry of Education G1 Mathematics syllabus. G1 is a Mathematics subject level under Full Subject-Based Banding, not a fixed label for a learner’s potential. Schools can teach and assess topics in different sequences.
For Bukit Timah families: Bring a marked Maths question to a parent-student consultation and ask which first wrong step needs attention. Contact eduKate Singapore to enquire about current G1 tutorial suitability, class times and availability.