Grade 4 Area and Perimeter word problems | Grade1to6.com - Free Printable

Let's solve each problem step by step and explain the solutions clearly.

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1. A square has sides that are 9 feet long. What is the area of the box?

Given:
- Side of square = 9 feet

Formula for Area of a Square:
> Area = side × side
> or
> Area = $ l \times b $

Since it’s a square, length = breadth = 9 feet.

$$
\text{Area} = 9 \times 9 = 81 \text{ square feet}
$$

✔ Answer: $ \boxed{81} $ square feet

> ⚠️ Note: The image says "81 sq cm", but the unit should be square feet, since the side is in feet. So the correct answer is 81 sq ft.

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2. A rectangular box is 7 centimeters long and 4 centimeters wide. What is its perimeter?

Given:
- Length ($l$) = 7 cm
- Width ($b$) = 4 cm

Formula for Perimeter of a Rectangle:
> Perimeter = $ 2 \times (l + b) $

$$
= 2 \times (7 + 4) = 2 \times 11 = 22 \text{ cm}
$$

✔ Answer: $ \boxed{22} $ cm

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3. Find the width of the book. The book's perimeter is 40 cm.

We are given:
- Perimeter = 40 cm
- But we don’t know the length or width — so we need more information.

Wait! This problem seems incomplete unless we assume something like it's a rectangle with known length or it's a square.

But since no other info is given, perhaps it's implied that the book is a rectangle, and maybe we're missing a value?

Let’s suppose the length is not given, so we can't determine the width uniquely without more data.

But if the question expects us to find width, maybe it's assumed the book is a square?

Let’s check:

If it were a square:
- Perimeter = $ 4 \times \text{side} $
- $ 40 = 4 \times s \Rightarrow s = 10 $

So width = 10 cm

But this assumes it's a square — which isn't stated.

Alternatively, if it's a rectangle and only perimeter is given, we cannot determine width alone without knowing length.

But since this is Grade 4, likely there's an assumption: maybe the length is given elsewhere, or perhaps it's a typo.

Wait — let’s recheck: “Find the width of the book. The book’s perimeter is 40 cm.”

This is insufficient unless more is known.

But perhaps it's implied that length is known from context? Not here.

So this problem is incomplete as stated.

However, if we assume the book is a square, then:

$$
\text{Side} = \frac{40}{4} = 10 \text{ cm}
$$

So width = $ \boxed{10} $ cm

But again, this is an assumption.

👉 Conclusion: Problem 3 is ambiguous. It needs either length or shape information.

But assuming it's a square (common in such problems), then:

✔ Answer (assumed): $ \boxed{10} $ cm

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4. The perimeter of a table is 70 cm, find the width and length of the table.

Again, only perimeter is given: 70 cm

We need two variables (length and width), but only one equation.

$$
P = 2(l + b) = 70 \Rightarrow l + b = 35
$$

So $ l + b = 35 $ cm

But without more info (like ratio, or one dimension), there are infinite possible answers.

For example:
- If $ l = 20 $, $ b = 15 $
- If $ l = 25 $, $ b = 10 $
- etc.

So this problem is incomplete.

Unless it's assumed the table is a square, then:

$$
4s = 70 \Rightarrow s = 17.5 \text{ cm}
$$

Then both length and width = $ \boxed{17.5} $ cm

But again, this is an assumption.

👉 Conclusion: Without more info, cannot uniquely determine length and width.

But if assumed square:
✔ Answer (assumed): Length = Width = $ \boxed{17.5} $ cm

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5. A rectangular table is 24 centimeters long and 2 centimeters wide. What is its perimeter?

Given:
- Length = 24 cm
- Width = 2 cm

Perimeter formula:
> $ P = 2(l + b) $

$$
= 2(24 + 2) = 2 \times 26 = 52 \text{ cm}
$$

✔ Answer: $ \boxed{52} $ cm

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6. The lake around your house is 75 meters long and 35 meters wide. What is its perimeter?

Given:
- Length = 75 m
- Width = 35 m

$$
P = 2(l + b) = 2(75 + 35) = 2 \times 110 = 220 \text{ m}
$$

✔ Answer: $ \boxed{220} $ meters

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✔ Final Answers Summary:

| Question | Answer |
|--------|--------|
| 1 | 81 sq ft |
| 2 | 22 cm |
| 3 | Incomplete – assuming square: 10 cm |
| 4 | Incomplete – assuming square: 17.5 cm each |
| 5 | 52 cm |
| 6 | 220 m |

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🔍 Notes:

- Problems 3 and 4 are underdetermined without additional assumptions.
- In real-world contexts, especially at Grade 4 level, if only perimeter is given and asked for dimensions, often the shape is assumed to be square.
- Always ensure units match: e.g., feet vs cm vs meters.

Let me know if you'd like these problems rewritten with proper assumptions or diagrams!