Free original lessons
Area of Irregular Shapes on Grid Paper
This free printable pack gives students four closed rectilinear shapes drawn on an integer grid. Each grid square stands for one square unit, so area can be found by counting enclosed squares or by splitting the shape into rectangles. The pack includes a reference sheet, a student sheet and an answer sheet, each supplied separately for A4 and US Letter paper, plus one SVG per page.
Letter & A4
PDF & SVG
Every outline is a closed rectilinear polygon whose corners sit on integer grid intersections, which keeps counting and rectangle decomposition straightforward. The reference sheet works through Task 1 as a guided example: it counts the enclosed unit squares strip by strip from the bottom row upward (6 + 6 + 3 + 3 + 3) to reach 21 square units, and it notes that recounting each horizontal strip checks the result. The student sheet presents the same four tasks with a deliberate blank attempt area for working, so students can draw a decomposition or record strip counts before writing an answer. The answer sheet gives the area for each task together with the strip-count reasoning and a check method. A square represents one square unit, not one physical square centimetre, so treat the grid as a unit grid rather than a ruler. The shoelace areas agree independently with the unit-cell counts, which supports the answers but is not needed by students.
Download the complete resource pack
All individual editable SVG pages (18)
- A4 reference page 1
- A4 student page 1
- A4 student page 2
- A4 student page 3
- A4 student page 4
- A4 answer page 1
- A4 answer page 2
- A4 answer page 3
- A4 answer page 4
- LETTER reference page 1
- LETTER student page 1
- LETTER student page 2
- LETTER student page 3
- LETTER student page 4
- LETTER answer page 1
- LETTER answer page 2
- LETTER answer page 3
- LETTER answer page 4
Print at 100% / actual size. Use the stated scale on any schematic diagram; physical cutting templates are identified separately. A4 and US Letter are separate files. Free access, no signup; CC BY 4.0.
How to use these pages
- Choose the paper size you need and print the reference sheet first; read the worked Task 1 example to see how strip counting and rectangle decomposition are recorded.
- Print the student sheet and have students attempt each shape in the blank attempt area, either counting enclosed unit squares row by row or splitting the outline into rectangles.
- Ask students to check each answer by recounting the horizontal strips so every enclosed square is counted exactly once.
- Use the answer sheet to compare areas and reasoning, discussing any task where the count and the decomposition disagree.
Four practice tasks and complete answers
Task 1
Find the area of the outlined shape in the Task 1 diagram. Each grid square is 1 square unit. Show a rectangle decomposition or count the enclosed unit squares.
Show answer 1
21 square units.
Count from the bottom row upward: 6 + 6 + 3 + 3 + 3 = 21 enclosed unit squares.
Check: Recount each horizontal strip; every enclosed square is counted exactly once, giving 21 square units.
Task 2
Find the area of the outlined shape in the Task 2 diagram. Each grid square is 1 square unit. Show a rectangle decomposition or count the enclosed unit squares.
Show answer 2
26 square units.
Count from the bottom row upward: 7 + 7 + 4 + 4 + 4 = 26 enclosed unit squares.
Check: Recount each horizontal strip; every enclosed square is counted exactly once, giving 26 square units.
Task 3
Find the area of the outlined shape in the Task 3 diagram. Each grid square is 1 square unit. Show a rectangle decomposition or count the enclosed unit squares.
Show answer 3
24 square units.
Count from the bottom row upward: 8 + 5 + 5 + 2 + 2 + 2 = 24 enclosed unit squares.
Check: Recount each horizontal strip; every enclosed square is counted exactly once, giving 24 square units.
Task 4
Find the area of the outlined shape in the Task 4 diagram. Each grid square is 1 square unit. Show a rectangle decomposition or count the enclosed unit squares.
Show answer 4
24 square units.
Count from the bottom row upward: 6 + 6 + 4 + 4 + 2 + 2 = 24 enclosed unit squares.
Check: Recount each horizontal strip; every enclosed square is counted exactly once, giving 24 square units.
Useful checks
- Counting a square twice where strips meet, or missing a square at a step in the outline; recounting strip by strip catches both.
- Treating a grid square as one physical square centimetre; here it is one square unit only.
- Splitting the shape into rectangles that overlap or leave gaps, which changes the total; check that the parts cover the outline exactly once.
Questions about this resource
What is the area of the Task 1 shape?
21 square units. The reference sheet counts the enclosed unit squares from the bottom row upward as 6 + 6 + 3 + 3 + 3, and recounting each horizontal strip confirms the total.
Do I need to use rectangle decomposition?
No. Counting enclosed unit squares is enough, and the answer sheet's check method uses horizontal strip counts. Rectangle decomposition is an alternative way to reach the same area.