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

Let’s solve each problem one by one, step by step. We’ll use the formulas for area and perimeter of a rectangle:

- Area = length × width
- Perimeter = 2 × (length + width)

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Problem 1:

Length = 16 ft
Width = 12 ft

Area = 16 × 12 = 192 ft²
Perimeter = 2 × (16 + 12) = 2 × 28 = 56 ft

✔ Answer: Area = 192 ft², Perimeter = 56 ft

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Problem 2:

Width = 30 cm
Length = 40 cm

Area = 40 × 30 = 1200 cm²
Perimeter = 2 × (40 + 30) = 2 × 70 = 140 cm

✔ Answer: Area = 1200 cm², Perimeter = 140 cm

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Problem 3:

Length = 8 cm
Width = 6 cm

Area = 8 × 6 = 48 cm²
Perimeter = 2 × (8 + 6) = 2 × 14 = 28 cm

✔ Answer: Area = 48 cm², Perimeter = 28 cm

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Problem 4:

Width = 250 m
Length = 500 m

We only need perimeter here (for the fence).

Perimeter = 2 × (500 + 250) = 2 × 750 = 1500 m

✔ Answer: Perimeter = 1500 m

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Problem 5:

Area = 150 m²
Length = 25 m

First, find width:
Width = Area ÷ Length = 150 ÷ 25 = 6 m

Now find perimeter:
Perimeter = 2 × (25 + 6) = 2 × 31 = 62 m

✔ Answer: Width = 6 m, Perimeter = 62 m

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Problem 6:

Area = 5200 ft²
Width = 75 ft

Find length:
Length = Area ÷ Width = 5200 ÷ 75

Let’s calculate that:

75 × 69 = 5175 → too low
75 × 70 = 5250 → too high
So try 5200 ÷ 75:

Divide: 5200 ÷ 75 = 69.333...? Wait — let’s do it properly.

Actually, 75 × 69 = 5175
5200 - 5175 = 25 → so 69 + 25/75 = 69 + 1/3 ≈ 69.333… but we should check if it divides evenly.

Wait — maybe I made a mistake. Let me recalculate:

5200 ÷ 75

Divide numerator and denominator by 25:
5200 ÷ 25 = 208
75 ÷ 25 = 3
→ So 208 ÷ 3 = 69.333…? That can’t be right for a real orchard dimension? But mathematically, it’s correct.

But wait — let me double-check: 75 × 69.333… = 75 × (208/3) = (75/3) × 208 = 25 × 208 = 5200 ✔

So length = 208/3 ft or 69⅓ ft. But since the problem doesn’t specify to round, we can leave as fraction or decimal.

However, in word problems like this, sometimes they expect exact values. Let’s write it as a mixed number or improper fraction.

But actually — let me check again: Is 5200 divisible by 75?

75 = 25 × 3
5200 ÷ 25 = 208 → yes
208 ÷ 3 = 69.333… → not whole number.

But the problem says “find the length”, so we must give the exact value.

So:

Length = 5200 ÷ 75 = 208 ÷ 3 = 69⅓ ft

But perhaps we should write it as a decimal rounded? The problem doesn’t say. Since other answers are whole numbers, maybe I misread?

Wait — let me re-read Problem 6:

“The area of an apple orchard is 5200 ft². Find the length of the rectangular orchard, if it's width is 75 ft.”

No mention of rounding. So we must give exact answer.

But 5200 ÷ 75 simplifies:

Divide numerator and denominator by 25:
5200 ÷ 25 = 208
75 ÷ 25 = 3
→ 208/3 ft = 69 1/3 ft

Alternatively, as decimal: 69.333... ft

But in school math, often they prefer fractions unless specified.

However, looking back at all other problems — they all resulted in whole numbers. Maybe there’s a typo? Or maybe I should just compute it correctly.

Wait — let me calculate 75 × 69.333... = 75 × 69 + 75 × 1/3 = 5175 + 25 = 5200 ✔ Correct.

So length is 208/3 ft or 69 1/3 ft.

But perhaps the problem expects us to write it as a decimal? Or maybe I should check if 5200 ÷ 75 reduces.

Actually, 5200 ÷ 75 = 1040 ÷ 15 = 208 ÷ 3 → same thing.

I think for accuracy, we'll write it as a fraction.

But let me see — maybe the problem meant 5250? No, it says 5200.

Okay, we’ll go with exact value.

So:

Length = 5200 ÷ 75 = 208/3 ft = 69 1/3 ft

But since the question only asks for length (not perimeter), we stop here.

✔ Answer: Length = 208/3 ft or 69 1/3 ft

But to match format of other answers, perhaps write as decimal? However, in math class, fractions are preferred when exact.

Alternatively, maybe I made a calculation error earlier? Let me verify once more:

75 × 69 = 5175
5200 - 5175 = 25
25 / 75 = 1/3 → so 69 + 1/3 = 69 1/3 → correct.

So final answer for #6 is 69 1/3 ft.

But let’s write it as an improper fraction or mixed number? Mixed number is clearer.

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Final Answers:

1. Area = 192 ft², Perimeter = 56 ft
2. Area = 1200 cm², Perimeter = 140 cm
3. Area = 48 cm², Perimeter = 28 cm
4. Perimeter = 1500 m
5. Width = 6 m, Perimeter = 62 m
6. Length = 69 1/3 ft (or 208/3 ft)

But for consistency, since others are whole numbers, and this is a word problem, perhaps they expect decimal? But no instruction.

Actually, let me check online or standard practice — in such worksheets, if division isn't exact, they usually accept fraction or decimal. But since 1/3 is repeating, better to write as fraction.

Alternatively, maybe I should write it as 69.33 ft? But that’s approximate.

The problem says "find the length", so exact value is best.

I’ll go with 69 1/3 ft.

But to make it neat, let’s write all answers clearly.

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Final Answer:
1. Area = 192 ft², Perimeter = 56 ft
2. Area = 1200 cm², Perimeter = 140 cm
3. Area = 48 cm², Perimeter = 28 cm
4. Perimeter = 1500 m
5. Width = 6 m, Perimeter = 62 m
6. Length = 69 1/3 ft