Area and Perimeter Worksheets by Shelly Rees worksheets library - Free Printable

Let's solve the problems on this Winter Perimeter & Area Worksheet for 3rd–4th grade. We'll go step by step through each section.

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🌟 Left Worksheet: "Missing Side"

#### 🔹 Problem 1:
- Shape: Rectangle
- Given sides: 20 (top), 20 (bottom), missing left and right sides.
- Perimeter = 48

Formula for perimeter of a rectangle:
$$ P = 2 \times (l + w) $$

We know two sides are 20, so the other two must be equal (rectangle). Let’s call the missing side $ x $.
So:
$$
P = 20 + 20 + x + x = 48 \\
40 + 2x = 48 \\
2x = 8 \\
x = 4
$$

✔ Answer: Missing sides = 4

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#### 🔹 Problem 2:
- Shape: Rectangle
- Given sides: 2 (left), 2 (right), missing top and bottom
- Perimeter = 24

Let missing side = $ x $

$$
P = 2 + 2 + x + x = 24 \\
4 + 2x = 24 \\
2x = 20 \\
x = 10
$$

✔ Answer: Missing sides = 10

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#### 🔹 Problem 3:
- Square with one side = 9
- Perimeter = 40

Wait — a square has four equal sides, so if each side is 9, then:

$$
P = 4 \times 9 = 36
$$

But the problem says perimeter = 40 → contradiction?

Wait! The shape is not necessarily a square — it's labeled as “Find the missing sides” with only one side given.

But in the diagram, both horizontal sides are 9, and vertical sides are unknown. So it's a rectangle with width = 9, height = ?

Let height = $ x $

Perimeter:
$$
P = 2(9 + x) = 40 \\
18 + 2x = 40 \\
2x = 22 \\
x = 11
$$

✔ Answer: Missing sides = 11

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#### 🔹 Problem 4:
- Rectangle: One side = 15 (top and bottom), missing left and right
- Perimeter = 64

Let missing side = $ x $

$$
P = 2(15 + x) = 64 \\
30 + 2x = 64 \\
2x = 34 \\
x = 17
$$

✔ Answer: Missing sides = 17

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#### 🔹 Problem 5:
- Rectangle: Length = 12, Width = 5
- Find perimeter and area

Perimeter:
$$
P = 2(12 + 5) = 2(17) = 34
$$

Area:
$$
A = l \times w = 12 \times 5 = 60
$$

✔ Answer: Perimeter = 34, Area = 60

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#### 🔹 Problem 6:
- Two rectangles:
- First: 7 × 5
- Second: 2 × 13

Find perimeter of each

First rectangle:
$$
P = 2(7 + 5) = 2(12) = 24
$$

Second rectangle:
$$
P = 2(2 + 13) = 2(15) = 30
$$

✔ Answer: Perimeters = 24 and 30

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🌟 Right Worksheet: "Winter Perimeter"

Now calculate perimeters of various winter-themed shapes.

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#### 🔹 Snowman 1:
- Top hat: 5 units wide
- Middle block: 9 units high, 5 units wide?
- Bottom block: 10 units wide, 7 units high?

Wait — let's interpret carefully.

The snowman is made of three rectangles stacked:

- Top (hat): width = 5, height = ? (but we don’t need height for perimeter unless it's a full rectangle)
- Middle: height = 9, width = ?
- Bottom: height = 7, width = 10

But the perimeter of the entire snowman figure? Or just the outer edge?

Actually, looking at the layout, the instruction says: "Calculate the perimeter of the shapes" and draw a line to the correct answer.

But no options are visible here — perhaps they're implied or on another page.

However, we can compute the perimeter of each individual shape.

Let’s assume we’re to find the perimeter of the outer outline of each shape.

But since these are compound figures, we need to be careful.

Alternatively, maybe it's asking for the perimeter of each component.

But let's try to interpret each one.

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#### 🔹 Snowman 1 (Top):
- Hat: rectangle, width = 5, height = 5? (assuming from drawing)
- But not enough info — perhaps we're meant to treat the entire snowman as a composite shape, but without clear dimensions.

Wait — the numbers are labeled:

- Top: 5 (width), 5 (height)? Not clear.

But looking again:

Snowman 1:
- Top: 5 (width), 5 (height) — probably a small rectangle
- Middle: 9 (height), 5 (width) — but width not labeled
- Bottom: 10 (width), 7 (height)

But the snowman’s total outline is complex.

Alternatively, maybe the problem is to find the perimeter of the front view of the snowman.

But without clear edges, it's hard.

Wait — perhaps the shapes are separate, like:

- The first snowman has:
- Top block: 5×5
- Middle: 9×5
- Bottom: 10×7

But they are stacked, so overlapping sides are internal.

To find total perimeter of the whole snowman, you add all outer edges.

But that’s complicated.

Alternatively, maybe the problem wants us to calculate the perimeter of each rectangular block separately.

But the instruction says: “Calculate the perimeter of the shapes” — likely meaning each individual shape.

But the snowman is composed of three rectangles.

Wait — look at the second snowman:

- Top: 3 (width), 3 (height)?
- Middle: 6 (height), 3 (width)?
- Bottom: 7 (height), 4 (width)?

Again, not fully labeled.

But notice: the first snowman has numbers: 5, 9, 7, 10

Let’s assume:

- Top rectangle: width = 5, height = 5 (from the hat)
- Middle rectangle: width = 5, height = 9
- Bottom rectangle: width = 10, height = 7

But the middle and bottom have different widths — so it's not aligned.

So the total shape has an irregular outline.

But instead, perhaps the intended task is to find the perimeter of each rectangle separately.

But the worksheet says “draw a line to the correct answer” — so there must be multiple-choice answers off-screen.

Since we can't see them, we’ll compute what we can.

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#### 🔹 Ice Cube (Cube):
- All sides = 6
- But it says: “Calculate the perimeter of the front of the ice cube.”

Front face is a square with side = 6

So perimeter of a square:
$$
P = 4 \times 6 = 24
$$

✔ Answer: P = 24

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#### 🔹 Star:
- Blue star, labeled with side = 2
- But how many sides? A typical 5-pointed star has 10 sides (if counting each edge).

But usually, such problems consider each point as having a length.

But here, it says “side = 2”, and it’s a regular star.

Assuming it's a regular pentagram, it has 10 equal sides.

But without knowing how many sides, we can’t compute.

Alternatively, maybe it’s a regular polygon with 5 sides?

But it looks like a 5-pointed star.

But perhaps the intended interpretation is: each straight segment is 2 units, and there are 10 segments.

Then:
$$
P = 10 \times 2 = 20
$$

But that’s speculative.

Alternatively, if it’s a regular star with 5 points, and each side is 2, then yes, 10 sides.

But let’s suppose it’s a simple star with 5 outer points, and each side is 2 → total 10 sides.

✔ Answer: P = 20 (if 10 sides)

But if it's a pentagon, 5 sides × 2 = 10

But it's a star, so more likely 10 sides.

But we’ll go with P = 20 as a reasonable assumption.

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#### 🔹 Snowflake:
- Labeled “1” — probably radius or side?
- It’s a complex snowflake pattern.

But often, such problems simplify it as a hexagon or symmetric shape.

But here, it’s labeled “1” — perhaps each arm is 1 unit long?

But without clear structure, hard to say.

Alternatively, maybe it’s a regular hexagon with side 1?

Then perimeter = 6 × 1 = 6

But it’s a snowflake, so maybe 6 arms, each with length 1?

But still, unclear.

Perhaps the intended answer is 6.

But let’s move on.

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#### 🔹 Pink Square:
- “Each side of the square is 4”
- So it’s a square with side = 4

Perimeter:
$$
P = 4 \times 4 = 16
$$

✔ Answer: P = 16

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✔ Final Answers Summary

#### Left Worksheet:

| Problem | Answer |
|--------|--------|
| 1 | Missing sides = 4 |
| 2 | Missing sides = 10 |
| 3 | Missing sides = 11 |
| 4 | Missing sides = 17 |
| 5 | Perimeter = 34, Area = 60 |
| 6 | Perimeters = 24 and 30 |

#### Right Worksheet:

| Shape | Perimeter |
|-------|----------|
| Ice cube (front) | 24 |
| Star (assumed 10 sides × 2) | 20 |
| Snowflake (assume 6 sides × 1) | 6 |
| Pink square | 16 |

> ⚠️ Note: The snowman and snowflake perimeters depend on assumptions due to lack of clear labeling. If the worksheet includes multiple-choice answers, students would match these computed values.

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🎉 Conclusion:

This worksheet helps students practice:
- Finding missing sides using perimeter
- Calculating perimeter and area of rectangles
- Understanding that perimeter is the sum of all sides
- Applying concepts to fun winter-themed shapes

Let me know if you'd like a printable version or visual explanation! ❄️📘