AC9M4M02 • Homework

Perimeter and Area of Shapes and Enclosed Spaces worksheet

Use this printable homework sheet for written working, application and reflection alongside the online learning activities.

Open practice

Eight written homework tasks

Each task stands alone and may appear in any order in the PDF. Use separate paper for larger drawings and practical records. Ask an adult to inspect actual measuring and making as well as written answers.

  1. For the 7 cm by 4 cm rectangle, trace the full boundary and write a sum of all four sides to find the perimeter. Find the area by counting rows of squares. Explain why the perimeter and area use different units.

  2. On separate square grid paper, draw two rectangles with different side-length pairs that each cover 18 square units. Label every side in grid units, calculate each perimeter by adding the four sides, and compare. Explain what stays the same and what can change.

  3. Draw a closed shape with curved and straight boundary sections on separate paper. Fit string around its whole edge, mark the meeting point and measure the straightened string. Repeat the measurement. Record both lengths with units, give an approximate perimeter and explain a possible source of variation or why the readings agree.

  4. Count the full squares and partial squares covered by the blue shape. Show how to combine the edge pieces into whole units and give the area. Explain why counting every touched square as a full unit would give a different answer.

  5. Use one paper square repeatedly to measure a rectangle and a triangle you draw on separate paper. Trace or mark and number every placement. State the unit’s size. For each shape, record the whole-square count, combined part count and total area or a justified estimate. Explain how you avoided gaps and overlaps.

  6. Draw a 6 cm by 2 cm rectangle on separate grid paper. Show how 1 cm square units cover it, then group the same surface into 2 cm by 2 cm paper-square units. Record both tile counts and the area in cm². Explain why changing the unit changes the count but not the surface.

  7. A drawn pond outline covers 18 whole grid squares and parts of 9 more squares. Explain why its area is between 18 and 27 square units. The edge pieces together cover about 4 whole units. Give a sensible area estimate and explain why it is an approximation. How could a finer grid help?

  8. ALFA’s public 2020 report describes Mimal Rangers using mapped land patches in wildfire planning. For an invented class map, patch A covers 11 whole squares and 2 halves; patch B covers 9 whole squares and 6 halves of the same unit. Compare their areas and show the combined parts. Explain why this map alone cannot choose a real burn location.

Complete answer guide and practical checks

  1. Perimeter: 7 + 4 + 7 + 4 = 22 cm. Area: four rows of seven squares = 28 cm². Centimetres measure boundary length; square centimetres measure surface coverage. Require a complete traced boundary, four-side sum, organised area count and unit explanation.

  2. Examples: 3 by 6 has perimeter 18 units; 2 by 9 has perimeter 22 units. Both areas are 18 square units. A 1 by 18 rectangle (perimeter 38) is also valid. Inspect both actual drawings, distinct dimension pairs, four labelled sides, correct sums and the comparison: area stays fixed while boundary length can change.

  3. Actual shapes and measurements vary. Example: 52 cm and 54 cm support about 53 cm. Inspect the closed drawing with both curved and straight sections, complete string placement, two real unit-labelled measurements and a sensible estimate. A relevant explanation could describe careful repeat placement, a gap at a curve or string stretching.

  4. The top row contains four full squares and a half; the bottom contains three full squares and a half. Seven full squares plus two halves make 8 square units. Counting all nine touched squares as full gives 9, overcounting the two half-square regions. Require full/part counts, combination and the explanation.

  5. Answers vary with the drawings. Example with a 1 cm square: a 4 cm by 2 cm rectangle covers 8 cm²; a triangle covering three whole squares and three halves covers 4½ cm². Inspect actual repeated use of one square on both shapes, marked placements, stated unit, full/part records, totals and no-gap/no-overlap explanation. Accept other valid shapes and carefully justified estimates.

  6. There are 12 small 1 cm squares, so the area is 12 cm². The same rectangle is covered by three 2 cm by 2 cm square units. Each large square covers four small squares; 3 × 4 = 12 cm². Inspect the actual labelled drawing and grouping without gaps/overlaps. Require both counts and explanation that the unchanged surface uses fewer larger units.

  7. The partial pieces add more than zero but less than nine full squares, so the area is more than 18 and less than 27 square units. With about four whole units from parts, estimate about 22 square units. The pieces were judged approximately, so do not call 22 exact. Smaller grid units can follow the boundary in finer detail and reduce the size of uncertain edge pieces.

  8. A: 11 + 1 = 12 square units. B: 9 + 3 = 12 square units. Neither patch is larger; the areas are equal. Require both fractional combinations and square units. The map is invented and supports only an area comparison. Actual burn decisions need authorised local expertise and other site information; the class data do not give those.

Accept valid alternative constructions and real measurements that match the chosen objects. A completion tick alone does not demonstrate the required practical evidence.