Perimeter and Area Grade 3 online exercise for - Free Printable

Let's solve each problem step by step.

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Part 1: Find the area by counting the squares.

We'll count the number of unit squares for Area, and then calculate the Perimeter by counting the outer edges (each side of a square is 1 unit).

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#### 1. Blue rectangle
- It has 3 rows × 4 columns = 12 squares
- Area: 12
- Perimeter: Count all outer edges:
- Top: 4, Bottom: 4, Left: 3, Right: 3 → Total = 4 + 4 + 3 + 3 = 14
- Perimeter: 14

✔ Area: 12, Perimeter: 14

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#### 2. Green square
- 3 rows × 3 columns = 9 squares
- Area: 9
- Perimeter: 3 + 3 + 3 + 3 = 12
- Perimeter: 12

✔ Area: 9, Perimeter: 12

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#### 3. Purple rectangle
- 3 rows × 5 columns = 15 squares
- Area: 15
- Perimeter: 5 + 5 + 3 + 3 = 16
- Perimeter: 16

✔ Area: 15, Perimeter: 16

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#### 4. Pink shape (L-shaped)
- Count the squares:
- Bottom row: 4 squares
- Middle: 2 squares (stacked)
- Top: 2 squares
- Total = 4 + 2 + 2 = 8 squares
- Area: 8
- Perimeter: Trace the outer edges.
- Start from bottom-left:
- Bottom: 4 units
- Right side: up 2 units (to middle), then right 1, up 1, left 1, down 1, right 1, up 1, left 1, down 1, left 1
- Easier to count:
- Each exposed edge is 1 unit.
- Count all sides touching outside:
- Bottom: 4
- Right: 3 (vertical)
- Top: 2 (right top)
- Left: 3 (left side)
- Then the indent: add 2 more horizontal and 2 vertical?
- Better method: trace around.
- Bottom: 4
- Right: 3 (from bottom to top)
- Top: 2 (top row)
- Left: 2 (middle column)
- But there’s an inward step: at the top-left, it goes in.
- Let's count carefully:
- Bottom: 4
- Right: 3 (up)
- Top: 2 (right to left)
- Then left: 2 (down)
- Then go down 1, left 1, down 1, left 1, down 1
- Wait — better to use formula or visual count.

Actually, let's do this:
- The shape has:
- 4 on bottom
- 2 in center (stacked)
- 2 on top
- So total: 4+2+2 = 8 ✔
- Now perimeter:
- Draw it mentally:
```
_ _ _
_ _ _
_ _ _ _
```
Actually:
- Row 1: 2 squares (top)
- Row 2: 2 squares (middle)
- Row 3: 4 squares (bottom)

So:
```
□□
□□
□□□□
```

Now trace outer edges:

- Start bottom-left:
- Go right: 4 units
- Up: 1 unit (to middle row)
- Right: 0? No — we are at end of row 3
- From bottom-right corner:
- Up: 2 units (to top of middle column)
- Left: 1 unit (to second column)
- Up: 1 unit (to top)
- Left: 2 units (to start)
- Down: 2 units (to bottom)
- Left: 1 unit (to first column)
- Down: 1 unit (to bottom-left)
- Back to start?

Let's list all outer edges:
- Bottom: 4
- Right side: from bottom to top: 3 units (since 3 rows tall on right)
- Top: 2 units (only two squares on top)
- Left side: from top to bottom: 2 units (but indented)
- But also, the inner steps contribute.

Use counting all exposed sides:
- Each small square has 4 sides.
- But shared sides are internal.

Total sides: 8 squares × 4 = 32
Subtract shared sides:
- Horizontal shared: between adjacent squares
- Bottom row: 3 shared (between 4 squares)
- Middle row: 1 shared (between 2 squares)
- Top row: 1 shared
- Between rows:
- Bottom-middle: 2 shared (column 1 and 2)
- Middle-top: 2 shared
- Total shared edges: 3 + 1 + 1 + 2 + 2 = 8
- Each shared edge removes 2 sides (one from each square)
- So total removed: 8 × 2 = 16
- Outer edges: 32 - 16 = 16
- So Perimeter = 16

✔ Area: 8, Perimeter: 16

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#### 5. Blue U-shape
- Shape:
```
□□□
□
□□□
```
- Count squares:
- Top: 3
- Middle: 1
- Bottom: 3
- Total = 7
- Area: 7

Now perimeter:
- Again, count outer edges or trace.

Visual:
- Top: 3
- Right: 1 (top), then down 1 (middle), then down 1 (bottom) → total 3
- Bottom: 3
- Left: 1 (bottom), up 1 (middle), up 1 (top) → 3
- But the middle is missing, so the inner sides are exposed.

Better: trace the boundary.

Start at top-left:
- Right: 3
- Down: 1 (to middle)
- Right: 1 (into middle)
- Down: 1 (to bottom)
- Left: 1
- Down: 1
- Left: 1
- Up: 1
- Left: 1
- Up: 1
- Right: 1
- Up: 1
- Right: 1
- Up: 1
- Back?

Wait — simpler:
- Each square contributes 4 sides, but subtract shared ones.

Total sides: 7 × 4 = 28
Shared edges:
- Horizontal:
- Top row: 2 shared (between 3 squares)
- Bottom row: 2 shared
- Middle: none
- Vertical:
- Column 1: top and bottom connected? No — only one in middle
- Column 2: top and middle? No — not aligned
- Column 3: same
- Only if they're stacked vertically.

So:
- Vertical shared:
- Column 1: top and bottom? Not connected — gap in middle
- Column 2: no vertical connection
- Column 3: no
- So no vertical shared edges?

Wait — actually:
- Top row: positions 1,2,3
- Middle: position 2 only
- Bottom: positions 1,2,3

So:
- Column 1: top and bottom — not connected
- Column 2: top, middle, bottom — yes! All three stacked?
- Top: row 1, col 2
- Middle: row 2, col 2
- Bottom: row 3, col 2
- So vertical shared edges: 2 (top-middle, middle-bottom)
- Column 1: only top and bottom — not connected
- Column 3: same

So vertical shared: 2 edges

Horizontal:
- Top row: 2 shared (between 1-2, 2-3)
- Bottom row: 2 shared
- Middle row: only 1 square → no shared
- So horizontal shared: 4

Total shared edges: 2 (vertical) + 4 (horizontal) = 6
Each shared edge removes 2 sides → 6 × 2 = 12
Outer sides: 28 - 12 = 16

But wait — the U-shape has an open center. The inner edges are exposed.

Wait — actually, when two squares are adjacent, they share a side, which is not part of perimeter.

But here:
- Top row: squares 1-2 and 2-3 → 2 shared
- Bottom row: 1-2 and 2-3 → 2 shared
- Middle: only one square → no horizontal
- Vertical:
- Col 2: top and middle → shared
- Col 2: middle and bottom → shared
- So 2 vertical shared

Total shared: 6 → 6 × 2 = 12 sides removed
Total outer sides: 28 - 12 = 16

So Perimeter = 16

✔ Area: 7, Perimeter: 16

---

#### 6. Yellow stepped shape
- Count squares:
- Row 1 (top): 3
- Row 2: 4
- Row 3: 5
- Row 4: 6
- Total = 3+4+5+6 = 18 squares
- Area: 18

Now perimeter:
- This is a staircase-like shape, going down to the right.

Trace the outer boundary:
- Top: 3
- Right: 6 (since 4 rows)
- Bottom: 6
- Left: 3 (but with steps)
- But the left side has steps upward.

Actually, it's like a right triangle shape.

From the pattern:
- Each row increases by 1
- It's a staircase from top-left to bottom-right

To find perimeter:
- Top edge: 3
- Right edge: 6 (height)
- Bottom edge: 6
- Left edge: 3
- But the inner steps contribute additional edges.

Wait — better: count all exposed sides.

Use the method:
- Total sides: 18 × 4 = 72
- Shared edges:
- Horizontal: within rows
- Row 1: 2 shared
- Row 2: 3 shared
- Row 3: 4 shared
- Row 4: 5 shared
- Total horizontal: 2+3+4+5 = 14
- Vertical: between rows
- Column 1: 3 connections (row1-2, 2-3, 3-4) → 3
- Column 2: 3 connections
- Column 3: 3 connections
- Column 4: 2 (only rows 2-3, 3-4)
- Column 5: 1 (rows 3-4)
- Column 6: 0
- So vertical shared:
- Col1: 3
- Col2: 3
- Col3: 3
- Col4: 2
- Col5: 1
- Total = 3+3+3+2+1 = 12

Total shared edges: 14 (horizontal) + 12 (vertical) = 26
Each shared edge removes 2 sides → 26 × 2 = 52
Outer sides: 72 - 52 = 20

So Perimeter = 20

✔ Area: 18, Perimeter: 20

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Part 2: Find the area by multiplying length × width

#### 7. Rectangle: 9 mm × 5 mm
- Area = length × width = 9 × 5 = 45 mm²
✔ Area: 45 mm²

#### 8. Rectangle: 2 cm × 8 cm
- Area = 2 × 8 = 16 cm²
✔ Area: 16 cm²

#### 9. Square: 7 m × 7 m
- Area = 7 × 7 = 49 m²
✔ Area: 49 m²

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✔ Final Answers:

#### Part 1: Count Squares
| # | Area | Perimeter |
|---|------|-----------|
| 1 | 12 | 14 |
| 2 | 9 | 12 |
| 3 | 15 | 16 |
| 4 | 8 | 16 |
| 5 | 7 | 16 |
| 6 | 18 | 20 |

#### Part 2: Multiply Length × Width
| # | Area |
|---|--------------|
| 7 | 45 mm² |
| 8 | 16 cm² |
| 9 | 49 m² |

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