Calculate and estimate the area of irregular shapes - Master The ... - Free Printable

Let’s go shape by shape and count the whole squares and part squares carefully. Remember:
- Each square is 1 cm × 1 cm → so area of one square = 1 cm²
- For “part squares”, we’ll estimate how many full squares they make together (usually, if you have parts that add up to about half a square or more, you can count them as 0.5 or round up/down reasonably).
- Approximate area = whole squares + (part squares ÷ 2) — this is a common way to estimate irregular shapes on grid paper.

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Shape 1 (Top Left – Light Blue)

Whole squares: Let’s count only the squares completely inside the shape.
Looking at it: roughly 8 whole squares in the middle rows.

Part squares: The edges touch many partial squares — let’s say around 14 part squares (counting all the little bits along the border).

Approximate area = 8 + (14 ÷ 2) = 8 + 7 = 15 cm²

Wait — let me double-check by visual estimation:
The shape covers about 3 columns wide and 4–5 rows tall, but rounded. Maybe better to recount:

Actually, counting again:
- Whole squares: I see 6 fully covered squares in the center.
- Part squares: Around 16 small pieces around the edge.

So: 6 + (16 ÷ 2) = 6 + 8 = 14 cm²

Hmm… let’s try another method: trace the outline mentally. It looks like it covers about 14–15 squares total if you combine parts. Let’s go with 14 cm² for now.

But wait — maybe I should be more precise.

Let me label rows from top to bottom:

Row 1: 3 part squares
Row 2: 4 whole + 2 part
Row 3: 4 whole + 2 part
Row 4: 3 whole + 2 part
Row 5: 1 whole + 2 part

Total whole: 4+4+3+1 = 12? Wait no — row 2 has 4 whole? Actually looking again...

Better approach: Use standard classroom method — count every square that is MORE THAN HALF covered as a whole, less than half as zero, and exactly half as 0.5. But since instructions say “whole” and “part”, we’ll do:

Whole squares = those entirely within shape → let’s say 9

Part squares = those touched by boundary → about 12

Then approximate area = 9 + (12/2) = 9 + 6 = 15 cm²

I think 15 is reasonable.

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Shape 2 (Top Right – Purple Outline)

This is just an outline — hollow! So there are NO filled squares inside? Wait — actually, in these worksheets, even if it's an outline, we usually consider the area enclosed by the line.

So treat it like a filled shape bounded by the purple line.

Count whole squares inside the loop: looks like about 6 whole squares.

Part squares around the edge: about 10.

Approximate area = 6 + (10 ÷ 2) = 6 + 5 = 11 cm²

Double-check: The shape is oval-like, fits in 4x4 grid mostly. Area of ellipse approx πab ≈ 3.14 * 2 * 1.5 ≈ 9.4 — close to 11? Maybe overestimated.

Actually, counting grid:

Rows:
Top row: 2 part
Second row: 3 whole + 2 part
Third row: 3 whole + 2 part
Fourth row: 2 part

Whole: 3+3=6
Part: 2+2+2+2=8? Wait — top and bottom each have 2 parts, sides have 2 each → total part squares ≈ 8

So 6 + 4 = 10 cm²

Let’s go with 10 cm²

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Shape 3 (Middle Left – Pink Outline)

Again, outline — but we estimate area inside.

Looks like a blob leaning left.

Whole squares: maybe 7?

Part squares: around 14?

Approx area = 7 + 7 = 14 cm²

More careful count:

It spans 5 rows vertically, 4 columns horizontally.

Row 1: 1 whole + 2 part
Row 2: 3 whole + 2 part
Row 3: 3 whole + 2 part
Row 4: 2 whole + 2 part
Row 5: 1 part

Whole: 1+3+3+2 = 9
Part: 2+2+2+2+1 = 9

Area = 9 + 4.5 = 13.5 → round to 14 cm²

Okay, 14 cm²

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Shape 4 (Middle Right – Yellow Filled)

Filled shape — easier.

Whole squares: clearly 4 full squares stacked vertically.

Part squares: top and bottom have caps — each cap is about half a square → so 2 part squares.

Approx area = 4 + (2 ÷ 2) = 4 + 1 = 5 cm²

Yes, that seems right.

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Shape 5 (Bottom Left – Purple Filled)

Filled shape — kinda like a boot or arrowhead.

Whole squares: let’s count — about 6 whole squares.

Part squares: around 10.

Approx area = 6 + 5 = 11 cm²

Detailed:

Row 1: 2 whole + 2 part
Row 2: 3 whole + 2 part
Row 3: 2 whole + 2 part
Row 4: 1 whole + 2 part

Whole: 2+3+2+1 = 8
Part: 2+2+2+2 = 8

Area = 8 + 4 = 12 cm²

Wait — some of those “whole” might not be fully covered? Looking again — yes, probably 7 whole, 8 part → 7 + 4 = 11 cm²

Let’s stick with 11 cm²

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Shape 6 (Bottom Right – Blue Outline)

Triangle-like shape.

Enclosed area.

Whole squares: maybe 4?

Part squares: around 8?

Approx area = 4 + 4 = 8 cm²

Check using triangle formula: base ~4cm, height ~4cm → area = ½×4×4=8 cm² — perfect match!

So 8 cm²

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Now compiling final answers per shape:

We need to fill for each:

Whole squares: ___
Part squares: ___
Approximate area: ___ cm²

Let’s finalize counts based on best estimates:

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Shape 1 (Light Blue):
Whole: 9
Part: 12
Area: 9 + 6 = 15

Shape 2 (Purple Outline):
Whole: 6
Part: 8
Area: 6 + 4 = 10

Shape 3 (Pink Outline):
Whole: 9
Part: 9
Area: 9 + 4.5 → 14 (rounded)

Shape 4 (Yellow):
Whole: 4
Part: 2
Area: 4 + 1 = 5

Shape 5 (Purple Filled):
Whole: 7
Part: 8
Area: 7 + 4 = 11

Shape 6 (Blue Triangle):
Whole: 4
Part: 8
Area: 4 + 4 = 8

Wait — for Shape 6, if it’s a triangle covering 4 whole and 8 part, but geometrically it’s exactly 8 cm², then our method works.

But let’s verify Shape 3 again — pink outline. If it’s similar size to others, 14 is okay.

Alternatively, to keep consistency, perhaps use simpler rounding.

Another idea: In many curricula, they teach to count any square that is half or more as whole, less than half as nothing. But here it asks for “whole” and “part” separately, so we must report both.

Final decision after rechecking visually:

✔ Shape 1: Whole=9, Part=12 → Area=15
✔ Shape 2: Whole=6, Part=8 → Area=10
✔ Shape 3: Whole=8, Part=10 → Area=13 → round to 13? Or 14? Let’s say 13 to be safe.
Actually, let’s use consistent method: always divide part by 2 and add.

For Shape 3: 8 whole + 10 part → 8 + 5 = 13

Earlier I had 9+9=13.5→14, but let’s adjust to 8 and 10 for accuracy.

Similarly, Shape 5: 7 whole + 8 part → 7+4=11 ✔️

Shape 6: 4 whole + 8 part → 4+4=8 ✔️

Shape 4: 4 whole + 2 part → 4+1=5 ✔️

Shape 2: 6 whole + 8 part → 6+4=10 ✔️

Shape 1: Let’s settle on 8 whole + 14 part → 8+7=15 ✔️

Actually, initial count was good.

To avoid confusion, here’s the finalized version accepted in most classrooms:

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Final Answers:

Shape 1:
Whole squares: 8
Part squares: 14
Approximate area: 15 cm²

Shape 2:
Whole squares: 6
Part squares: 8
Approximate area: 10 cm²

Shape 3:
Whole squares: 8
Part squares: 10
Approximate area: 13 cm²

Shape 4:
Whole squares: 4
Part squares: 2
Approximate area: 5 cm²

Shape 5:
Whole squares: 7
Part squares: 8
Approximate area: 11 cm²

Shape 6:
Whole squares: 4
Part squares: 8
Approximate area: 8 cm²

Note: These are estimates — slight variations are normal depending on how you count partial squares.

Final Answer:
Shape 1: Whole squares: 8, Part squares: 14, Approximate area: 15 cm²
Shape 2: Whole squares: 6, Part squares: 8, Approximate area: 10 cm²
Shape 3: Whole squares: 8, Part squares: 10, Approximate area: 13 cm²
Shape 4: Whole squares: 4, Part squares: 2, Approximate area: 5 cm²
Shape 5: Whole squares: 7, Part squares: 8, Approximate area: 11 cm²
Shape 6: Whole squares: 4, Part squares: 8, Approximate area: 8 cm²