Did you know? Cutting a rectangular notch out of a shape can make its area smaller while making its perimeter longer. That may sound surprising until you draw every boundary. Composite figures teach students to distinguish what is inside a shape from what goes around it.
For parents searching for a Secondary 3 G1 Mathematics tutor in Bukit Timah, this guide connects classroom methods with questions students can actually explain. G1 is a subject level in Singapore’s Full Subject-Based Banding system. The SEAB 2027 G1 syllabus directory lists Mathematics as K110, and the official Mathematics syllabus specifies whole-course content. Your child’s school determines the Secondary 3 teaching order and current assessment scope.
Quick answer: break a complex shape into simple parts
A composite plane figure is a flat region formed from simpler shapes, such as rectangles, triangles or parts of circles. The 2027 G1 K110 syllabus includes perimeter and area of composite plane figures. To calculate an area, add the pieces that belong to the region or subtract the pieces that have been removed. To calculate a perimeter, follow the actual exposed outline.
An internal line where two shapes meet is not generally part of the outside boundary. Likewise, a gap cut into the side may create new exposed edges. These are geometry decisions, not simply arithmetic decisions.
Worked example 1: a rectangular panel with a central notch
Question. Imagine a rectangular panel 12 cm wide and 8 cm high. A rectangular notch 4 cm wide and 3 cm deep is cut into the middle of its top edge. The cut reaches inward from the top but does not touch either side of the panel. Find the remaining area and the full perimeter of the notched outline.
- Start with the original rectangular area: 12 × 8 = 96 cm².
- Find the missing notch area: 4 × 3 = 12 cm².
- Subtract: 96 − 12 = 84 cm² of material remains.
- Find the original outer perimeter: 2(12 + 8) = 40 cm.
- Account for the notch: the original 4 cm top segment is replaced by two 3 cm vertical sides and a 4 cm inner horizontal edge.
- Calculate the new perimeter: 40 − 4 + 3 + 4 + 3 = 46 cm.
The notch removes 12 cm² of area but introduces six centimetres of extra boundary length. Students often calculate the area correctly and assume the perimeter must also become smaller. This example shows why that assumption fails.
Why drawing the notch matters
The phrase ‘a notch in the middle of the top edge’ tells us that the indentation creates three exposed inner edges: two sides and a bottom. The 4 cm stretch of the original top edge is no longer part of the region’s boundary. A quick sketch with a highlighter following the entire outline helps prevent double-counting.
If the same rectangle were cut in a different position, the perimeter result could change. Geometry problems must be read as descriptions of actual shapes, not just lists of numbers.
Worked example 2: a cut-out at a corner
Question. A 10 cm by 7 cm rectangle has a 4 cm by 3 cm rectangle removed from the upper-right corner. The cut follows the rectangle’s horizontal and vertical sides. Find the remaining area and perimeter.
- Original area: 10 × 7 = 70 cm².
- Removed corner area: 4 × 3 = 12 cm².
- Remaining L-shaped area: 70 − 12 = 58 cm².
- Original perimeter: 2(10 + 7) = 34 cm.
- Perimeter change: removing 4 cm from the upper edge and 3 cm from the right edge creates a new internal step with edges of those same lengths.
- New perimeter: 34 − 4 − 3 + 4 + 3 = 34 cm.
Here the area decreases but the perimeter stays the same. Compare that with the first example, where a notch in the middle increases the perimeter. The position of a cut matters, even when the removed piece has a familiar rectangular shape.
Worked example 3: a rectangle topped by a semicircle
Imagine a fictional sign consisting of a 6 cm wide, 4 cm high rectangle with a semicircle attached along its full 6 cm top edge. The semicircle has diameter 6 cm, so its radius is 3 cm.
- Rectangle area: 6 × 4 = 24 cm².
- Semicircle area: (1/2)π × 3² = 4.5π cm².
- Combined area: 24 + 4.5π ≈ 38.1 cm² to three significant figures.
- External straight boundary: the bottom is 6 cm and the two sides are 4 cm each, totalling 14 cm.
- Curved semicircle boundary: half of 2πr = π × 3 = 3π cm.
- Perimeter: 14 + 3π ≈ 23.4 cm.
The 6 cm line joining the rectangle to the semicircle is inside the composite figure, so it is not added again to the outer perimeter. The same line matters for positioning the pieces, but not as an exposed edge.
Three general strategies for composite shapes
Strategy 1: add the pieces
When simple shapes sit beside each other without overlapping, calculate their areas separately and add them. This works for a rectangle connected to a semicircle or two rectangular wings of an L-shaped floor plan.
Strategy 2: subtract a missing region
When a piece has been removed from a larger rectangle or circle, subtract the missing area from the original. This works well for notches, cut-out corners and simple openings.
Strategy 3: trace the exposed outline for perimeter
Perimeter is not usually the sum of every component’s individual perimeter. Shared internal edges must not be counted as exterior boundaries. Trace the real outline in one continuous direction and record every exposed segment once.
Why units are a built-in checking tool
Area measures a flat region and uses square units. Perimeter measures a boundary and uses ordinary length units. A result such as 84 cm² answers an area question; 46 cm answers a perimeter question. Swapping the units is a warning that the quantities may have been confused.
If the dimensions mix centimetres and metres, convert them to one compatible unit before calculating. When converting a final area from cm² to m², remember the factor is 10,000, not 100.
Four errors a tutor should investigate
Counting an internal join as exposed boundary
The full 6 cm straight top of the rectangle beneath the semicircle is hidden inside the joined shape. Including it in perimeter would overcount.
Subtracting area but leaving the old perimeter unchanged automatically
A central notch creates new edges; a corner cut may replace equal edge lengths. Inspect the geometry rather than assuming every subtraction changes the perimeter in the same way.
Using the diameter as the semicircle’s radius
A diameter of 6 cm means radius 3 cm. Using 6 in πr² would make the circular area four times too large.
Losing the requested unit
Keep the distinction between centimetres and square centimetres visible through the working, and apply the final rounding instruction only at the end.
A 12-minute practice plan
- Sketch a 12 cm by 8 cm rectangle and mark a 4 cm by 3 cm central top notch.
- Calculate the remaining area first.
- Trace the entire notched outline and calculate its perimeter.
- Repeat with a corner cut-out and explain why the perimeter behaves differently.
- Sketch a rectangle with a semicircle on top and circle the hidden joining edge.
- Finish by explaining, in one sentence, why area and perimeter may change in different directions.
Questions Bukit Timah parents often ask
Are composite plane figures part of G1 Mathematics?
Yes. The K110 syllabus specifically includes problems involving perimeter and area of composite plane figures.
Is the quickest method always to divide a figure into rectangles?
Not always. Adding pieces or subtracting a cut-out can both work. Choose whichever accurately represents the diagram and produces simpler calculations.
How can a tutor tell whether the idea has been understood?
Change the cut-out from a corner to the middle of a side. The learner should predict the effect on perimeter before calculating, then justify the result by tracing the boundary.
A practical next step for Bukit Timah families
Ask your child to show one recent school problem and identify the first working step that is hard to explain. The unchanged eduKateSG small-group Mathematics tutorial reference describes guided corrections and close tutor attention near Sixth Avenue MRT, for its Secondary 1 Clementi programme. It does not confirm that a particular Secondary 3 G1 class or place is currently available. Contact eduKate Singapore to ask about an appropriate arrangement.
Continue reading this Secondary 3 G1 Mathematics series
- Ratios with Fractions and Decimals
- Graphing Linear Equations in Two Variables
- Collecting and Classifying Data Correctly
- geometry and measurement without guesswork
Official reference: SEAB’s 2027 G1 Mathematics K110 syllabus.