Let’s solve each problem one by one. We’ll use the formulas for area and perimeter of rectangles:
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Perimeter = 2 × (length + width)
-
Area = length × width
We’ll also remember that if we know the perimeter and one side, we can find the other side — and same with area.
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Problem 1:
Peter’s desk is 48 inches long and 36 inches wide. What is the perimeter?
→ Perimeter = 2 × (48 + 36)
= 2 × 84
=
168 inches
✔ Check: 48 + 36 = 84; 84 × 2 = 168 → Correct.
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Problem 2:
Our backyard is 12 feet long and 10 feet wide. What is the area?
→ Area = 12 × 10 =
120 square feet
✔ Check: 12 × 10 is easy — 120 → Correct.
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Problem 3:
The perimeter of the basketball court is 288 feet. The width is 50 feet. What is the length?
→ Perimeter = 2 × (length + width)
So, 288 = 2 × (length + 50)
Divide both sides by 2:
144 = length + 50
Subtract 50 from both sides:
length = 144 - 50 =
94 feet
✔ Check: 2 × (94 + 50) = 2 × 144 = 288 → Correct.
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Problem 4:
The area of my math text book is 48 square inches. The book is 8 inches long. How wide is it?
→ Area = length × width
48 = 8 × width
Divide both sides by 8:
width = 48 ÷ 8 =
6 inches
✔ Check: 8 × 6 = 48 → Correct.
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Problem 5:
The perimeter of the living room is 40 feet. The width is 10 feet. What is the area?
First, find the length.
→ Perimeter = 2 × (length + width)
40 = 2 × (length + 10)
Divide both sides by 2:
20 = length + 10
Subtract 10:
length = 10 feet
Now, area = length × width = 10 × 10 =
100 square feet
✔ Check: Perimeter = 2×(10+10)=40 → correct. Area = 10×10=100 → correct.
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Problem 6:
The area of this town is 42 square miles. The length is 7 miles. What is the perimeter?
First, find the width.
→ Area = length × width
42 = 7 × width
Divide by 7:
width = 42 ÷ 7 =
6 miles
Now, perimeter = 2 × (length + width) = 2 × (7 + 6) = 2 × 13 =
26 miles
✔ Check: Area = 7×6=42 → correct. Perimeter = 2×13=26 → correct.
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Final Answer:
1. 168 inches
2. 120 square feet
3. 94 feet
4. 6 inches
5. 100 square feet
6. 26 miles
Parent Tip: Review the logic above to help your child master the concept of 4th grade area and perimeter worksheets.
