Area of a Rectangle Word Problem worksheet | Grade1to6 - Free Printable

Let's solve each of the word problems step by step.

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Problem 14:

This is a school playground which is of 45 feet in width and 75 feet in length. How many squares of 500 square feet can you make and will there be any space left after making these squares of 500 square feet each? What will be the space left if at all?

#### Step 1: Find the total area of the playground
The playground is rectangular, so:
$$
\text{Area} = \text{length} \times \text{width} = 75 \times 45 = 3375 \text{ square feet}
$$

#### Step 2: Divide total area by area of one square
Each square has an area of 500 square feet.
$$
\text{Number of squares} = \frac{3375}{500} = 6.75
$$

But we can only make whole squares, so we take the integer part:
$$
\text{Number of complete squares} = 6
$$

#### Step 3: Calculate the area used and remaining
- Area used: $6 \times 500 = 3000$ sq ft
- Space left: $3375 - 3000 = 375$ sq ft

✔ Answer:
- You can make 6 squares of 500 sq ft each.
- Yes, there will be space left.
- The leftover space is 375 square feet.

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Problem 15:

A square has an area of 81 square centimetres. How long is each side of the square?

#### Step 1: Use the formula for area of a square
$$
\text{Area} = \text{side}^2
$$
So,
$$
\text{side} = \sqrt{81} = 9 \text{ cm}
$$

✔ Answer: Each side is 9 centimeters long.

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Problem 16:

Li Jing bought 36 meters of fencing to make an enclosure for her pet dog, Tommy. If Li Jing expects a rectangular enclosure, what is the largest area it can have? Explain your answer.

#### Step 1: Understand the constraint
She has 36 meters of fencing, which is the perimeter of the rectangle.
$$
\text{Perimeter} = 2(l + w) = 36
\Rightarrow l + w = 18
$$

We want to maximize the area:
$$
\text{Area} = l \times w
$$

We can express $w = 18 - l$, so:
$$
\text{Area} = l(18 - l) = 18l - l^2
$$

This is a quadratic equation that opens downward (maximum at vertex).

The maximum occurs when $l = w = 9$ (i.e., a square).

So:
$$
\text{Maximum area} = 9 \times 9 = 81 \text{ square meters}
$$

✔ Answer:
- The largest area is 81 square meters.
- This happens when the enclosure is a square (9 m × 9 m).
- Explanation: For a given perimeter, a square gives the maximum area among all rectangles.

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Problem 17:

Li Jun has a rectangular garden that measures 10 feet by 18 feet. He wants to plant apples in his garden. His uncle said that one seed packet will be enough to fill a space 50 square feet. Will Li Jun’s garden have enough space to plant 4 seed packets?

#### Step 1: Find the area of the garden
$$
\text{Area} = 10 \times 18 = 180 \text{ square feet}
$$

#### Step 2: Find how much space 4 seed packets need
$$
4 \times 50 = 200 \text{ square feet}
$$

#### Step 3: Compare
- Garden area: 180 sq ft
- Required: 200 sq ft

Since $180 < 200$, the garden is not large enough.

✔ Answer:
- No, Li Jun’s garden does not have enough space to plant 4 seed packets.
- It needs 200 sq ft, but only has 180 sq ft.

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✔ Final Answers Summary:

| Problem | Answer |
|--------|--------|
| 14 | 6 squares can be made; 375 sq ft left |
| 15 | Each side is 9 cm |
| 16 | Largest area is 81 m² (when it's a square) |
| 17 | No, not enough space (needs 200 sq ft, has only 180) |

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