Math worksheet with four word problems on calculating perimeter and area of rectangles using fractions.

Let's solve each problem step by step.

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Problem 1:

Find the perimeter and area of a rectangle with width $6\frac{1}{2}$ cm and length 10 cm.

#### Step 1: Convert mixed numbers to improper fractions or decimals.
- Width = $6\frac{1}{2} = 6.5$ cm
- Length = 10 cm

#### Step 2: Use formulas:
- Perimeter of a rectangle:
$ P = 2 \times (\text{length} + \text{width}) $
$ P = 2 \times (10 + 6.5) = 2 \times 16.5 = 33 $ cm

- Area of a rectangle:
$ A = \text{length} \times \text{width} $
$ A = 10 \times 6.5 = 65 $ cm²

✔ Answer:
- Perimeter = 33 cm
- Area = 65 cm²

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Problem 2:

A small city park consists of a rectangular lawn that is $30\frac{1}{2}$ meters long and 20 meters wide. What is the area of the lawn?

#### Step 1: Convert mixed number to decimal.
- Length = $30\frac{1}{2} = 30.5$ m
- Width = 20 m

#### Step 2: Use area formula:
- $ A = \text{length} \times \text{width} $
- $ A = 30.5 \times 20 = 610 $ m²

✔ Answer:
- Area = 610 square meters

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Problem 3:

A rectangular swimming pool measures 16 meters by $8\frac{1}{4}$ meters. What is the area of the swimming pool?

#### Step 1: Convert mixed number to decimal.
- $8\frac{1}{4} = 8.25$ m

#### Step 2: Multiply length and width:
- $ A = 16 \times 8.25 $

Let’s compute:
- $ 16 \times 8 = 128 $
- $ 16 \times 0.25 = 4 $
- So, $ 128 + 4 = 132 $

✔ Answer:
- Area = 132 square meters

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Problem 4:

The rectangular top of a table is three times as long as it is wide. Its width is $1\frac{1}{2}$ meters. Find the area of the table top.

#### Step 1: Convert width to decimal.
- Width = $1\frac{1}{2} = 1.5$ m

#### Step 2: Find length.
- Length = 3 × width = $3 \times 1.5 = 4.5$ m

#### Step 3: Compute area.
- $ A = \text{length} \times \text{width} = 4.5 \times 1.5 $

Break it down:
- $ 4.5 \times 1.5 = (4 + 0.5)(1 + 0.5) $
- Or just multiply:
- $ 4.5 \times 1.5 = 6.75 $

✔ Answer:
- Area = 6.75 square meters

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✔ Final Answers:

1. Perimeter: 33 cm, Area: 65 cm²
2. Area of lawn: 610 m²
3. Area of pool: 132 m²
4. Area of table top: 6.75 m²

Let me know if you'd like these shown using fractions instead of decimals!