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

Let's solve each problem step by step.

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Problem 14:

Question: 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?

#### Solution:
1. Calculate the total area of the playground:
\[
\text{Area} = \text{Length} \times \text{Width} = 75 \, \text{feet} \times 45 \, \text{feet} = 3375 \, \text{square feet}
\]

2. Determine how many squares of 500 square feet can be made:
\[
\text{Number of squares} = \left\lfloor \frac{\text{Total Area}}{\text{Area of one square}} \right\rfloor = \left\lfloor \frac{3375}{500} \right\rfloor = \left\lfloor 6.75 \right\rfloor = 6
\]
So, 6 squares of 500 square feet can be made.

3. Calculate the total area covered by these 6 squares:
\[
\text{Total area covered} = 6 \times 500 = 3000 \, \text{square feet}
\]

4. Calculate the remaining space:
\[
\text{Remaining space} = \text{Total Area} - \text{Total area covered} = 3375 - 3000 = 375 \, \text{square feet}
\]

#### Final Answer for Problem 14:
\[
\boxed{6 \text{ squares, 375 square feet left}}
\]

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Problem 15:

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

#### Solution:
1. Use the formula for the area of a square:
\[
\text{Area} = \text{side}^2
\]
Given that the area is 81 square centimetres:
\[
\text{side}^2 = 81
\]

2. Solve for the side length:
\[
\text{side} = \sqrt{81} = 9 \, \text{cm}
\]

#### Final Answer for Problem 15:
\[
\boxed{9 \, \text{cm}}
\]

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Problem 16:

Question: 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.

#### Solution:
1. Understand the perimeter constraint:
The total length of the fencing is 36 meters, which is the perimeter of the rectangle.
\[
\text{Perimeter} = 2 \times (\text{Length} + \text{Width}) = 36
\]
Simplify:
\[
\text{Length} + \text{Width} = 18
\]

2. Express the area in terms of one variable:
Let the length be \( L \) and the width be \( W \). From the perimeter equation:
\[
W = 18 - L
\]
The area \( A \) of the rectangle is:
\[
A = L \times W = L \times (18 - L) = 18L - L^2
\]

3. Maximize the area:
The area function \( A = 18L - L^2 \) is a quadratic function that opens downwards (since the coefficient of \( L^2 \) is negative). The maximum value occurs at the vertex of the parabola.
The vertex of a parabola \( ax^2 + bx + c \) is at \( x = -\frac{b}{2a} \). Here, \( a = -1 \) and \( b = 18 \):
\[
L = -\frac{18}{2(-1)} = \frac{18}{2} = 9
\]
So, the length \( L = 9 \) meters. The width \( W \) is:
\[
W = 18 - L = 18 - 9 = 9 \, \text{meters}
\]

4. Calculate the maximum area:
\[
A = L \times W = 9 \times 9 = 81 \, \text{square meters}
\]

#### Final Answer for Problem 16:
\[
\boxed{81 \, \text{square meters}}
\]

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Problem 17:

Question: 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?

#### Solution:
1. Calculate the total area of the garden:
\[
\text{Area} = \text{Length} \times \text{Width} = 18 \, \text{feet} \times 10 \, \text{feet} = 180 \, \text{square feet}
\]

2. Determine the total area required for 4 seed packets:
Each seed packet covers 50 square feet, so 4 seed packets require:
\[
\text{Total area required} = 4 \times 50 = 200 \, \text{square feet}
\]

3. Compare the garden area with the required area:
The garden area is 180 square feet, and the required area is 200 square feet. Since 180 < 200, the garden does not have enough space to plant 4 seed packets.

#### Final Answer for Problem 17:
\[
\boxed{\text{No}}
\]

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Final Answers:

1. Problem 14: \(\boxed{6 \text{ squares, 375 square feet left}}\)
2. Problem 15: \(\boxed{9 \, \text{cm}}\)
3. Problem 16: \(\boxed{81 \, \text{square meters}}\)
4. Problem 17: \(\boxed{\text{No}}\)