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’re missing the length, so we can’t find the width unless we assume something. But this seems incomplete — we need either:
- The length, or
- Additional information (like it's a square or ratio)

But let’s suppose the length is known or implied. Since it's not given, perhaps it's a typo or missing data.

Wait — maybe it’s assumed that the book is a rectangle, and only perimeter is given? Then we cannot determine width alone without knowing length.

So unless more info is provided, this question is unsolvable as-is.

But let’s suppose the length is also given in another context. Wait — no, nothing else is mentioned.

Alternatively, maybe the length is 10 cm? Let's see if there's a common assumption.

Actually, let's check: Is it possible that the length is 10 cm?

Try solving:

Let length = $ l $, width = $ w $

Perimeter = $ 2(l + w) = 40 $

So:
$$
l + w = 20
\Rightarrow w = 20 - l
$$

Without knowing $ l $, we can't find $ w $. So this question is incomplete.

✘ Problem: Missing information (length of the book).

But wait — maybe the book is a square? If so, then:

Then all sides equal → $ 4s = 40 \Rightarrow s = 10 $ cm → width = 10 cm

But it says "book", which is usually rectangular.

So unless stated, we can’t assume it’s a square.

➡️ Conclusion: This problem is missing data — cannot be solved without knowing length.

But perhaps it was meant to say “the length is 12 cm” or something similar?

Let’s move on and come back.

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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, but no other information like ratio, area, or one dimension.

So again, infinite solutions exist.

For example:
- If length = 20 cm, then width = $ \frac{70}{2} - 20 = 35 - 20 = 15 $ cm
- If length = 25 cm, width = 10 cm
- etc.

So without additional constraints, we cannot uniquely determine length and width.

✘ Problem: Not enough information.

Unless it's implied that it's a square, then:

Perimeter = $ 4s = 70 \Rightarrow s = 17.5 $ cm → both length and width = 17.5 cm

But it says "table", not necessarily square.

So again, ambiguous.

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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

Formula:
> Perimeter = $ 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

Formula:
> Perimeter = $ 2(l + b) $

$$
= 2(75 + 35) = 2 \times 110 = 220 \text{ meters}
$$

✔ Answer: $ \boxed{220} $ meters

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## ✔ Summary of Answers:

| Question | Answer |
|--------|--------|
| 1 | 81 sq ft |
| 2 | 22 cm |
| 3 | ✘ Incomplete – missing length |
| 4 | ✘ Incomplete – need more info |
| 5 | 52 cm |
| 6 | 220 m |

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## 🔍 Notes:

- Question 1: The image shows "81 sq cm" but the side is in feet, so answer should be 81 sq ft.
- Questions 3 & 4 lack sufficient information to solve uniquely. They need either one dimension or an assumption (e.g., square shape).
- For Q3, if we assume the book is a square, then:
$$
4s = 40 \Rightarrow s = 10 \text{ cm} \Rightarrow \text{width} = 10 \text{ cm}
$$
But this is an assumption.
- For Q4, if we assume it's a square, then:
$$
4s = 70 \Rightarrow s = 17.5 \text{ cm}
$$
So both length and width = 17.5 cm.

But since these assumptions aren’t stated, they shouldn’t be made.

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## ✔ Final Correct Answers (with clarifications):

1. 81 sq ft
2. 22 cm
3. Cannot be determined (missing length)
4. Cannot be determined (missing information)
5. 52 cm
6. 220 m

If you have more details for Q3 and Q4 (e.g., length or shape), I can help refine them!