Area and Perimeter worksheet with six geometry problems for calculating area and perimeter of rectangles and triangles.

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 (or $ s^2 $)
- Perimeter = 4 × side

- Triangle:
- Area = $ \frac{1}{2} \times \text{base} \times \text{height} $
- Perimeter = sum of all three sides *(Note: Only base and height are given in some cases, so we assume only area is required 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 \times 4 = 40 \, \text{m}^2 $
- Perimeter = $ 2 \times (10 + 4) = 2 \times 14 = 28 \, \text{m} $

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

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2. Triangle: Base = 9m, Height = 6m

- Area = $ \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 9 \times 6 = 27 \, \text{m}^2 $

⚠️ We don't have the lengths of the other two sides, so perimeter cannot be calculated with given info.

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

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3. Square: Side = 7m

- Area = $ 7 \times 7 = 49 \, \text{m}^2 $
- Perimeter = $ 4 \times 7 = 28 \, \text{m} $

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

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4. Triangle: Base = 8m, Height = 12m

- Area = $ \frac{1}{2} \times 8 \times 12 = 4 \times 12 = 48 \, \text{m}^2 $

⚠️ Again, only base and height are given. No side lengths → perimeter not possible.

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

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5. Rectangle: 20m × 7m

- Area = $ 20 \times 7 = 140 \, \text{m}^2 $
- Perimeter = $ 2 \times (20 + 7) = 2 \times 27 = 54 \, \text{m} $

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

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6. Rectangle: 11m × 8m

- Area = $ 11 \times 8 = 88 \, \text{m}^2 $
- Perimeter = $ 2 \times (11 + 8) = 2 \times 19 = 38 \, \text{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 triangles #2 and #4, only base and height are provided, so we can compute area, but perimeter requires knowing all three side lengths — which aren’t given. So those perimeters are not solvable with current information.

Let me know if you'd like to estimate perimeter assuming it's an isosceles triangle!