Area and perimeter worksheet for students to solve equations for various shapes.

Sure! Let’s solve each problem step by step. We’ll calculate the Area and Perimeter for each shape using standard formulas.

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🔷 1. Rectangle (10m by 4m)

- Area of rectangle = length × width
→ 10m × 4m = 40 m²

- Perimeter of rectangle = 2 × (length + width)
→ 2 × (10 + 4) = 2 × 14 = 28 m

✔ Answer: Area = 40 m², Perimeter = 28 m

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🔷 2. Triangle (base = 9m, height = 6m)

*(Note: The 6m is shown as the height — the dashed line from vertex to base.)*

- Area of triangle = ½ × base × height
→ ½ × 9m × 6m = 4.5 × 6 = 27 m²

- Perimeter: We are only given base (9m) and height (6m), but not the side lengths. So we cannot calculate perimeter with the given info.

⚠️ *Important*: In many elementary worksheets, if only base and height are given for a triangle, they often expect only area, not perimeter — since perimeter requires all three sides.

✔ Answer: Area = 27 m², Perimeter = Not enough information

*(But if this worksheet expects you to assume it’s an isosceles triangle or use Pythagoras, it doesn’t specify. So safest answer is “not enough info” for perimeter.)*

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🔷 3. Square (side = 7m)

- Area of square = side × side
→ 7m × 7m = 49 m²

- Perimeter of square = 4 × side
→ 4 × 7m = 28 m

✔ Answer: Area = 49 m², Perimeter = 28 m

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🔷 4. Triangle (base = 8m, height = 12m)

*(Again, dashed line shows height.)*

- Area of triangle = ½ × base × height
→ ½ × 8m × 12m = 4 × 12 = 48 m²

- Perimeter: Only base and height given — sides not provided, so perimeter cannot be calculated.

✔ Answer: Area = 48 m², Perimeter = Not enough information

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🔷 5. Rectangle (20m by 7m)

- Area = length × width = 20m × 7m = 140 m²

- Perimeter = 2 × (length + width) = 2 × (20 + 7) = 2 × 27 = 54 m

✔ Answer: Area = 140 m², Perimeter = 54 m

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🔷 6. Rectangle (11m by 8m)

- Area = 11m × 8m = 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 | Shape | Area | Perimeter |
|---------|-------------|----------|---------------|
| 1 | Rectangle | 40 m² | 28 m |
| 2 | Triangle | 27 m² | Not enough info |
| 3 | Square | 49 m² | 28 m |
| 4 | Triangle | 48 m² | Not enough info |
| 5 | Rectangle | 140 m² | 54 m |
| 6 | Rectangle | 88 m² | 38 m |

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📌 Note for Problems 2 & 4 (Triangles):
If your teacher expects you to assume the triangle is isosceles and wants you to find the equal sides using the Pythagorean theorem, here’s how:

For Problem 2:
- Base = 9m → half-base = 4.5m
- Height = 6m
- Each equal side = √(4.5² + 6²) = √(20.25 + 36) = √56.25 = 7.5m
- Perimeter = 9 + 7.5 + 7.5 = 24 m

For Problem 4:
- Base = 8m → half-base = 4m
- Height = 12m
- Each equal side = √(4² + 12²) = √(16 + 144) = √160 ≈ 12.65m
- Perimeter ≈ 8 + 12.65 + 12.65 ≈ 33.3 m

But unless specified, it’s safer to say “not enough info” for perimeter on triangles when only base and height are given.

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✔ If this is for a younger student, likely only area is expected for the triangles.

Let me know if you want the “assume isosceles” version filled in too!