Here are the step-by-step solutions for each problem on the worksheet.
1) A rug had a length of 9 feet and a width of 3 feet. What is the perimeter of the rug?
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Formula: Perimeter = $2 \times (\text{Length} + \text{Width})$
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Step 1: Add the length and width: $9 + 3 = 12$ feet.
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Step 2: Multiply by 2: $12 \times 2 = 24$ feet.
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Answer: 24 ft
2) A piece of plywood was cut so its length was 6 feet by 2 feet. What is the area of the wood?
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Formula: Area = $\text{Length} \times \text{Width}$
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Step 1: Multiply the sides: $6 \times 2 = 12$.
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Step 2: Since it is area, use square units ($\text{ft}^2$).
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Answer: 12 $\text{ft}^2$
3) Rachel had a sheet of paper that was 9 inches long and 4 inches wide. What is the perimeter of the paper?
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Formula: Perimeter = $2 \times (\text{Length} + \text{Width})$
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Step 1: Add the length and width: $9 + 4 = 13$ inches.
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Step 2: Multiply by 2: $13 \times 2 = 26$ inches.
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Answer: 26 in
4) Carol was cutting out some fabric for a friend. She cut a piece that was 6 centimeters wide and had an area of 30 $\text{cm}^2$. How long was the piece?
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Formula: $\text{Area} = \text{Length} \times \text{Width}$ (so, $\text{Length} = \text{Area} \div \text{Width}$)
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Step 1: Divide the area by the width: $30 \div 6 = 5$.
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Answer: 5 cm
5) Tiffany had a sheet of paper that was 9 inches long and the area was 63 $\text{in}^2$. What is the width of the paper?
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Formula: $\text{Area} = \text{Length} \times \text{Width}$ (so, $\text{Width} = \text{Area} \div \text{Length}$)
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Step 1: Divide the area by the length: $63 \div 9 = 7$.
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Answer: 7 in
6) The woods behind Tom's house were 6 miles wide and 10 miles long. What is the area of the woods?
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Formula: Area = $\text{Length} \times \text{Width}$
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Step 1: Multiply the sides: $10 \times 6 = 60$.
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Step 2: Use square units ($\text{mi}^2$).
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Answer: 60 $\text{mi}^2$
7) Lana was cutting out some fabric for a friend. She cut a piece that was 7 centimeters wide and 6 centimeters long. What is the area of the fabric she cut out?
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Formula: Area = $\text{Length} \times \text{Width}$
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Step 1: Multiply the sides: $7 \times 6 = 42$.
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Step 2: Use square units ($\text{cm}^2$).
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Answer: 42 $\text{cm}^2$
8) An island in the Indian Ocean was 4 miles wide and 10 miles long. What is the perimeter of the island?
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Formula: Perimeter = $2 \times (\text{Length} + \text{Width})$
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Step 1: Add the length and width: $10 + 4 = 14$ miles.
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Step 2: Multiply by 2: $14 \times 2 = 28$ miles.
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Answer: 28 mi
9) The woods behind Victor's house were 5 miles wide and 6 miles long. What is the perimeter of the woods?
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Formula: Perimeter = $2 \times (\text{Length} + \text{Width})$
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Step 1: Add the length and width: $6 + 5 = 11$ miles.
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Step 2: Multiply by 2: $11 \times 2 = 22$ miles.
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Answer: 22 mi
10) A bathroom had a length of 2 feet and a total area of 6 $\text{ft}^2$. What is the width of the bathroom?
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Formula: $\text{Area} = \text{Length} \times \text{Width}$ (so, $\text{Width} = \text{Area} \div \text{Length}$)
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Step 1: Divide the area by the length: $6 \div 2 = 3$.
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Answer: 3 ft
Final Answer:
1. 24 ft
2. 12 $\text{ft}^2$
3. 26 in
4. 5 cm
5. 7 in
6. 60 $\text{mi}^2$
7. 42 $\text{cm}^2$
8. 28 mi
9. 22 mi
10. 3 ft
Parent Tip: Review the logic above to help your child master the concept of area and perimeter worksheet 6th grade.
