Area and perimeter worksheets (rectangles and squares) - Free Printable

Let's solve each problem step by step using the formulas for area and perimeter of different shapes.

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🔷 Formulas to Remember:

- Rectangle:
- Area = Length × Width
- Perimeter = 2 × (Length + Width)

- Square:
- Area = Side × Side = Side²
- Perimeter = 4 × Side

- Triangle:
- Area = ½ × Base × Height
- Perimeter = Sum of all three sides *(Note: Only given base and height in some cases — we’ll assume it's an isosceles triangle unless stated otherwise, but for area, only base and height are needed. For perimeter, we need all sides, so if not given, we can't calculate unless assumed or missing info is implied)*

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Now let’s go through each question:

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1. Rectangle: 20m × 4m

- Area = 20 × 4 = 80 m²
- Perimeter = 2 × (20 + 4) = 2 × 24 = 48 m

✔ Answer:
Area = 80 m²
Perimeter = 48 m

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2. Square: 10m side

- Area = 10 × 10 = 100 m²
- Perimeter = 4 × 10 = 40 m

✔ Answer:
Area = 100 m²
Perimeter = 40 m

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3. Rectangle: 9m × 3m

- Area = 9 × 3 = 27 m²
- Perimeter = 2 × (9 + 3) = 2 × 12 = 24 m

✔ Answer:
Area = 27 m²
Perimeter = 24 m

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4. Triangle: Base = 7m, Height = 8m

We're only given base and height. We can find area, but perimeter requires all three side lengths.

- Area = ½ × Base × Height = ½ × 7 × 8 = 28 m²

⚠️ Perimeter: Cannot be calculated without side lengths. But since this is a worksheet, likely assuming it's an isosceles triangle with two equal sides? But no information about side lengths is provided. So we can only compute area.

✔ Answer:
Area = 28 m²
Perimeter = Not enough info (but maybe expected to leave blank or assume?)

> However, sometimes in such problems, they might expect just the area if only base and height are given.

So:
- Area = 28 m²
- Perimeter = ??? → Can't determine

But let’s assume it's not required unless specified.

✔ Answer:
Area = 28 m²
Perimeter = [Not possible]

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5. Triangle: Base = 10m, Height = 12m

Same as above.

- Area = ½ × 10 × 12 = 60 m²
- Perimeter: Not enough data

✔ Answer:
Area = 60 m²
Perimeter = [Not possible]

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6. Square: 12m side

- Area = 12 × 12 = 144 m²
- Perimeter = 4 × 12 = 48 m

✔ Answer:
Area = 144 m²
Perimeter = 48 m

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7. Square: 4m side

- Area = 4 × 4 = 16 m²
- Perimeter = 4 × 4 = 16 m

✔ Answer:
Area = 16 m²
Perimeter = 16 m

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8. Rectangle: 11m × 3m

- Area = 11 × 3 = 33 m²
- Perimeter = 2 × (11 + 3) = 2 × 14 = 28 m

✔ Answer:
Area = 33 m²
Perimeter = 28 m

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## ✔ Final Answers Summary:

| Problem | Shape | Area | Perimeter |
|--------|--------------|------------|-----------|
| 1 | Rectangle | 80 m² | 48 m |
| 2 | Square | 100 m² | 40 m |
| 3 | Rectangle | 27 m² | 24 m |
| 4 | Triangle | 28 m² | ✘ (unknown) |
| 5 | Triangle | 60 m² | ✘ (unknown) |
| 6 | Square | 144 m² | 48 m |
| 7 | Square | 16 m² | 16 m |
| 8 | Rectangle | 33 m² | 28 m |

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📝 Notes:

- For triangles #4 and #5, only area can be computed because height and base are given, but side lengths are not.
- If you were told these are equilateral or isosceles, we could estimate, but without that, perimeter cannot be determined.

If this is a classroom worksheet, perhaps the teacher expects students to only compute area for triangles when only base and height are given.

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Let me know if you'd like a printable version or explanation for kids!