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

Let’s solve each problem one by one, step by step. We’ll use the formulas:

- Area of a rectangle = length × width
- Perimeter of a rectangle = 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 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 carefully:

75 × 69 = 5175 → too low
75 × 70 = 5250 → too high
So it’s between 69 and 70.

But let’s do exact division:

5200 ÷ 75 = ?

Divide numerator and denominator by 25:
5200 ÷ 25 = 208
75 ÷ 25 = 3
So 208 ÷ 3 = 69.333... or 69⅓ ft

Wait — maybe we made a mistake? Let me check again.

Actually, 75 × 69.333... = 75 × (208/3) = (75/3) × 208 = 25 × 208 = 5200 ✔

So length = 5200 ÷ 75 = 69.333... ft or 69⅓ ft

But since this is a word problem, maybe they expect a fraction or decimal?

Let’s write it as a mixed number: 69⅓ ft

Or if decimal: 69.33 ft (rounded to two decimals)

But let’s keep it exact: 69⅓ ft

However, in real-world contexts like orchards, sometimes they accept decimals.

But let’s double-check calculation:

75 × 69 = 5175
5200 - 5175 = 25
So 25/75 = 1/3 → so yes, 69⅓ ft

✔ Answer: Length = 69⅓ ft (or approximately 69.33 ft)

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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 = 69⅓ ft (or 69.33 ft)

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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 = 69⅓ ft