Area and Perimeter Worksheets | Grade1to6.com - Free Printable

Let's solve each of these Area & Perimeter Word Problems step by step.

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Problem 1:

The perimeter of a rectangular playground is 36 m. If the length of the park is 6 m, what is the width of the park?

#### ✔ Step-by-step Solution:
We use the formula for the perimeter of a rectangle:

$$
P = 2 \times (L + W)
$$

Where:
- $ P = 36 $ m
- $ L = 6 $ m
- $ W = ? $

Substitute into the formula:

$$
36 = 2 \times (6 + W)
$$

Divide both sides by 2:

$$
18 = 6 + W
$$

Subtract 6 from both sides:

$$
W = 12
$$

✔ Answer: The width of the park is 12 meters.

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Problem 2:

A rectangular room measures 15 m by 7 m. What is the area of this room?

#### ✔ Step-by-step Solution:
Use the formula for area of a rectangle:

$$
A = L \times W
$$

$$
A = 15 \times 7 = 105
$$

✔ Answer: The area of the room is 105 square meters.

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Problem 3:

Emily wants new carpeting for her room. Her room is a 12 ft by 12 ft rectangle. How much carpeting does she need to buy to cover her entire room?

#### ✔ Step-by-step Solution:
This is a square (since both sides are equal), but we still use the area formula:

$$
A = L \times W = 12 \times 12 = 144
$$

✔ Answer: Emily needs 144 square feet of carpeting.

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Problem 4:

Oliver is decorating the bulletin board in the school's lobby. The bulletin board is a 9 ft by 12 ft rectangle. He decides to add a black border around the entire bulletin board. What is the length of the border that he needs?

#### ✔ Step-by-step Solution:
The border goes around the edge, so we need the perimeter of the rectangle.

$$
P = 2 \times (L + W) = 2 \times (9 + 12) = 2 \times 21 = 42
$$

✔ Answer: The length of the border needed is 42 feet.

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Problem 5:

The school has a rectangular flower garden that is 5 meters long and 12 meters wide. One bag of fertilizer can cover 5 square meters. How many bags will the school need to buy to cover the entire garden?

#### ✔ Step-by-step Solution:
Step 1: Find the area of the garden.

$$
A = L \times W = 5 \times 12 = 60 \text{ square meters}
$$

Step 2: Each bag covers 5 sq m, so number of bags needed:

$$
\frac{60}{5} = 12
$$

✔ Answer: The school needs 12 bags of fertilizer.

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Problem 6:

The perimeter of a rectangular field is 80 ft and its width is 10 ft. Find the area of this field.

#### ✔ Step-by-step Solution:
We know:
- $ P = 80 $ ft
- $ W = 10 $ ft
- Need to find length (L) first using perimeter formula:

$$
P = 2(L + W)
$$

$$
80 = 2(L + 10)
$$

Divide both sides by 2:

$$
40 = L + 10
$$

Subtract 10:

$$
L = 30
$$

Now find the area:

$$
A = L \times W = 30 \times 10 = 300
$$

✔ Answer: The area of the field is 300 square feet.

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✔ Final Answers Summary:

| Problem | Answer |
|--------|--------|
| 1 | Width = 12 m |
| 2 | Area = 105 m² |
| 3 | Carpeting = 144 ft² |
| 4 | Border length = 42 ft |
| 5 | Bags needed = 12 |
| 6 | Area = 300 ft² |

Let me know if you'd like these problems explained with diagrams or visual aids!