Let’s solve each problem one by one, step by step.
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Problem 1:
The perimeter of a rectangular playground is 36 m. The length is 6 m. What is the width?
We know:
Perimeter of rectangle = 2 × (length + width)
So:
36 = 2 × (6 + width)
Divide both sides by 2:
18 = 6 + width
Subtract 6 from both sides:
width = 12 m
✔ Check: 2 × (6 + 12) = 2 × 18 = 36 → Correct!
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Problem 2:
A rectangular room measures 15 m by 7 m. What is the area?
Area of rectangle = length × width
= 15 × 7
= 105 square meters
✔ Check: 15 × 7 = 105 → Correct!
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Problem 3:
Emily’s room is 12 ft by 12 ft. How much carpeting does she need?
This is asking for area.
Area = 12 × 12 = 144 square feet
✔ Check: 12 × 12 = 144 → Correct!
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Problem 4:
Oliver wants to put a border around a 9 ft by 12 ft bulletin board. How long should the border be?
Border goes around the edge → that’s the perimeter.
Perimeter = 2 × (length + width)
= 2 × (9 + 12)
= 2 × 21
= 42 feet
✔ Check: 9+12+9+12 = 42 → Correct!
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Problem 5:
Flower garden is 5 meters long and 12 meters wide. One bag covers 5 sq meters. How many bags needed?
First, find area:
Area = 5 × 12 = 60 square meters
Each bag covers 5 sq meters → divide total area by 5:
60 ÷ 5 = 12 bags
✔ Check: 12 bags × 5 sq m = 60 sq m → Correct!
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Problem 6:
Perimeter of a rectangular field is 80 ft. Width is 10 ft. Find the area.
We know:
Perimeter = 2 × (length + width)
80 = 2 × (length + 10)
Divide both sides by 2:
40 = length + 10
Subtract 10:
length = 30 ft
Now find area:
Area = length × width = 30 × 10 = 300 square feet
✔ Check: Perimeter = 2×(30+10)=80 → Correct. Area = 30×10=300 → Correct!
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Final Answer:
1. 12 m
2. 105 m²
3. 144 ft²
4. 42 ft
5. 12 bags
6. 300 ft²
Parent Tip: Review the logic above to help your child master the concept of math area and perimeter worksheet.
