Let's solve each problem step by step using the formulas for
area and
perimeter of different shapes.
---
🔷 1. Rectangle (5m × 4m)
-
Area = length × width
$$
\text{Area} = 5\, \text{m} \times 4\, \text{m} = 20\, \text{m}^2
$$
-
Perimeter = 2 × (length + width)
$$
\text{Perimeter} = 2 \times (5 + 4) = 2 \times 9 = 18\, \text{m}
$$
✔ Answer:
- Area:
20 m²
- Perimeter:
18 m
---
🔷 2. Triangle (Base = 7m, Height = 5m)
This is a triangle with base and height given.
-
Area = $ \frac{1}{2} \times \text{base} \times \text{height} $
$$
\text{Area} = \frac{1}{2} \times 7\, \text{m} \times 5\, \text{m} = \frac{35}{2} = 17.5\, \text{m}^2
$$
⚠️ Note: We can't find perimeter without side lengths — only base and height are given. So we
cannot calculate perimeter from this info.
✔ Answer:
- Area:
17.5 m²
- Perimeter:
Not enough information
---
🔷 3. Rectangle (12m × 11m)
-
Area = length × width
$$
\text{Area} = 12\, \text{m} \times 11\, \text{m} = 132\, \text{m}^2
$$
-
Perimeter = 2 × (length + width)
$$
\text{Perimeter} = 2 \times (12 + 11) = 2 \times 23 = 46\, \text{m}
$$
✔ Answer:
- Area:
132 m²
- Perimeter:
46 m
---
🔷 4. Square (Side = 9m)
All sides are equal in a square.
-
Area = side²
$$
\text{Area} = 9\, \text{m} \times 9\, \text{m} = 81\, \text{m}^2
$$
-
Perimeter = 4 × side
$$
\text{Perimeter} = 4 \times 9 = 36\, \text{m}
$$
✔ Answer:
- Area:
81 m²
- Perimeter:
36 m
---
🔷 5. Triangle (Base = 6m, Height = 15m)
Again, base and height are given.
-
Area = $ \frac{1}{2} \times \text{base} \times \text{height} $
$$
\text{Area} = \frac{1}{2} \times 6\, \text{m} \times 15\, \text{m} = 3 \times 15 = 45\, \text{m}^2
$$
⚠️ Again, no side lengths → cannot compute perimeter.
✔ Answer:
- Area:
45 m²
- Perimeter:
Not enough information
---
🔷 6. Triangle (Base = 20m, Height = 10m)
-
Area = $ \frac{1}{2} \times \text{base} \times \text{height} $
$$
\text{Area} = \frac{1}{2} \times 20\, \text{m} \times 10\, \text{m} = 10 \times 10 = 100\, \text{m}^2
$$
⚠️ No side lengths →
cannot find perimeter
✔ Answer:
- Area:
100 m²
- Perimeter:
Not enough information
---
✔ Final Answers Summary:
| Problem | Shape | Area | Perimeter |
|--------|-------------|-------------|---------------|
| 1 | Rectangle | 20 m² | 18 m |
| 2 | Triangle | 17.5 m² | Not enough info |
| 3 | Rectangle | 132 m² | 46 m |
| 4 | Square | 81 m² | 36 m |
| 5 | Triangle | 45 m² | Not enough info |
| 6 | Triangle | 100 m² | Not enough info |
---
📝 Notes:
- For
triangles, if only
base and height are given, we can
only find area, not perimeter.
- For
rectangles and squares, both area and perimeter can be found with the given dimensions.
Let me know if you'd like a printable version or explanations in simpler terms!
Parent Tip: Review the logic above to help your child master the concept of 5th grade math worksheet area and perimeter.
