Your learning journey
Calculate perimeters and areas of compound rectilinear shapes, triangles, parallelograms and trapezia with correct units.
Follow the task-specific calculator guidance in Apply. Keyboard - means the same as −. Attempt before opening a scaffold or intentional practice explanation.
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Connect & Check
Perimeter: total boundary length. Area: surface coverage. Perpendicular height: shortest distance between parallel bases. Compound shape: shape assembled from familiar parts.
Intentional practice feedback after your attempt
20 cm.
2(6+4).
Intentional practice feedback after your attempt
24 cm².
6×4.
Intentional practice feedback after your attempt
100 mm².
10×10, not 10.
Present
A rectangle contains length×width unit squares. A triangle is half a parallelogram, so area=base×perpendicular height÷2. Shearing a parallelogram preserves area. Two matching trapezia make a parallelogram, giving area=(a+b)h÷2 for parallel sides a,b. Split compound shapes without overlap; internal cut lines do not count in the perimeter.
Label missing lengths. Trace the outer boundary for perimeter. For area, choose non-overlapping pieces or subtract a cut-out. State square units. Estimate and use a second partition to check.
Optional scaffold
Subtract removed area.
Intentional practice feedback after your attempt
52 cm².
60−8.
Optional scaffold
Height must be perpendicular.
Intentional practice feedback after your attempt
35 cm².
10×7÷2.
Optional scaffold
Sloping edge is not height.
Intentional practice feedback after your attempt
45 cm².
9×5.
Optional scaffold
Add only the parallel sides.
Intentional practice feedback after your attempt
28 cm².
(5+9)×4÷2.
Apply
Optional scaffold
Sketch the bounding parallelogram.
Intentional practice feedback after your attempt
40 cm² and 20 cm².
Triangle is half for equal base and height.
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52 cm²; 32 cm.
Removed boundary lengths are replaced by equal inset lengths; trace all six sides.
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34 m²; 68 tiles.
Divide area by coverage per tile.
Optional check: (5+9)×4÷2=28. Enter brackets round the sum. Estimate first; a triangle with the same base and height has half the parallelogram area.
Apply and extend
Intentional practice feedback after your attempt
4×4 gives perimeter 16 area16; 6×2 gives perimeter16 area12.
Same boundary length does not fix area.
Intentional practice feedback after your attempt
False: perimeter stays 32 cm; removed 4+2 is replaced by inset 4+2.
This refers to a corner cut, not any hole or notch.
Access, Scaffold, Core and Stretch support the same goal. Stretch deepens reasoning for either qualification tier.
Recall & Review
Retrieval without notes
Six retrieval points. Enter a number, decimal, fraction such as 3/2, or mixed number such as 1 1/2. Equivalent numeric values are accepted. Unsupported notation goes to teacher review. For rounding, also communicate the requested accuracy in written work; numerical scoring cannot judge significant trailing zeros.
Not checked.
Independent exit evidence
P1–P2: five minutes, no notes, 4 marks. Your teacher reviews working and explanations. Full assessment solutions are not embedded.
Recall & Review and prepare
A circle circumference is 2πr and area is πr². An arc or sector represents a fraction of the whole circle determined by its central angle divided by 360°.
Retrieve F1 again in one week. Bring your working and one question.
Your progress summary
Completion records attempts, not mastery. Retrieval points describe the latest checked attempt. Your teacher reviews P1–P2 separately and checks retained understanding after a delay.
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Optional extension activities
Allow 10–15 minutes if the main practice is secure. Show your method, explain a check and justify your conclusion.
Stretch
Reveal a worked check after attempting
Area=96−6=90 cm²; perimeter remains 40 cm for a corner notch.
Deep challenge
Reveal a worked check after attempting
No. A 6×6 square has perimeter 24 cm; a 4×9 rectangle has perimeter 26 cm.