Let's solve each problem step by step using the formulas for
area and
perimeter of different shapes.
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🔷 Formulas:
-
Rectangle:
- Area = length × width
- Perimeter = 2 × (length + width)
-
Square:
- Area = side × side
- Perimeter = 4 × side
-
Triangle:
- Area = (base × height) ÷ 2
- Perimeter = sum of all three sides *(Note: Only base and height are given in some cases, so we can only calculate area unless all sides are known.)*
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Now let’s go through each question:
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1. Rectangle: 10m × 4m
-
Area = length × width = 10 × 4 =
40 m²
-
Perimeter = 2 × (10 + 4) = 2 × 14 =
28 m
✔ Answer:
Area:
40 m²
Perimeter:
28 m
---
2. Triangle: base = 9m, height = 6m
-
Area = (base × height) ÷ 2 = (9 × 6) ÷ 2 = 54 ÷ 2 =
27 m²
⚠️ We don't have the lengths of the other two sides, so
we cannot compute perimeter with the given info.
✔ Answer:
Area:
27 m²
Perimeter:
Not enough information
---
3. Square: side = 7m
-
Area = side × side = 7 × 7 =
49 m²
-
Perimeter = 4 × side = 4 × 7 =
28 m
✔ Answer:
Area:
49 m²
Perimeter:
28 m
---
4. Triangle: base = 8m, height = 12m
-
Area = (base × height) ÷ 2 = (8 × 12) ÷ 2 = 96 ÷ 2 =
48 m²
⚠️ Again, no side lengths provided →
cannot find perimeter
✔ Answer:
Area:
48 m²
Perimeter:
Not enough information
---
5. Rectangle: 20m × 7m
-
Area = 20 × 7 =
140 m²
-
Perimeter = 2 × (20 + 7) = 2 × 27 =
54 m
✔ Answer:
Area:
140 m²
Perimeter:
54 m
---
6. Rectangle: 11m × 8m
-
Area = 11 × 8 =
88 m²
-
Perimeter = 2 × (11 + 8) = 2 × 19 =
38 m
✔ Answer:
Area:
88 m²
Perimeter:
38 m
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✔ Final Answers Summary:
| Problem | Area | Perimeter |
|--------|--------------|------------------|
| 1 | 40 m² | 28 m |
| 2 | 27 m² | Not enough info |
| 3 | 49 m² | 28 m |
| 4 | 48 m² | Not enough info |
| 5 | 140 m² | 54 m |
| 6 | 88 m² | 38 m |
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📝 Notes:
- For triangles, only
area can be found when base and height are given.
- To find
perimeter, you need the lengths of
all three sides.
- In problems 2 and 4, since only base and height are given (and not the side lengths), perimeter cannot be calculated.
Let me know if you'd like a version with answers filled in on the worksheet!
Parent Tip: Review the logic above to help your child master the concept of area and perimeter worksheet.
