Area and Perimeter worksheet for students to calculate the area and perimeter of various polygons.

Let's solve each polygon step by step, calculating both area and perimeter, and writing the number model (formula and calculation) for each.

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1. Rectangle: 15 in × 3 in

- Area:
Formula: $ \text{Area} = \text{length} \times \text{width} $
$ 15 \times 3 = 45 $
→ Area = 45 square inches

- Perimeter:
Formula: $ \text{Perimeter} = 2(\text{length} + \text{width}) $
$ 2(15 + 3) = 2(18) = 36 $
→ Perimeter = 36 inches

✔ Answer:
- Area = 45 in²
- Perimeter = 36 in

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2. Right Triangle: 6 cm, 10 cm, 11.7 cm

This is a right triangle with legs 6 cm and 10 cm, hypotenuse 11.7 cm.

- Area:
Formula: $ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} $
Use the two legs as base and height:
$ \frac{1}{2} \times 6 \times 10 = 30 $
→ Area = 30 cm²

- Perimeter:
Add all sides:
$ 6 + 10 + 11.7 = 27.7 $
→ Perimeter = 27.7 cm

✔ Answer:
- Area = 30 cm²
- Perimeter = 27.7 cm

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3. Rectangle: 4 ft × 5 ft

- Area:
$ 4 \times 5 = 20 $
→ Area = 20 ft²

- Perimeter:
$ 2(4 + 5) = 2(9) = 18 $
→ Perimeter = 18 ft

✔ Answer:
- Area = 20 ft²
- Perimeter = 18 ft

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4. Triangle: 5 m, 3 m, 6 m, height = 2 m

Base = 6 m, height = 2 m

- Area:
$ \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 6 \times 2 = 6 $
→ Area = 6 m²

- Perimeter:
Add all three sides:
$ 5 + 3 + 6 = 14 $
→ Perimeter = 14 m

✔ Answer:
- Area = 6 m²
- Perimeter = 14 m

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5. Parallelogram: base = 9 cm, height = 2 cm, side = 3 cm

Note: The slanted side is 3 cm, and the base is 9 cm. Height is 2 cm.

- Area:
Formula: $ \text{Area} = \text{base} \times \text{height} $
$ 9 \times 2 = 18 $
→ Area = 18 cm²

- Perimeter:
Opposite sides are equal. So two sides of 9 cm and two of 3 cm:
$ 2(9 + 3) = 2(12) = 24 $
→ Perimeter = 24 cm

✔ Answer:
- Area = 18 cm²
- Perimeter = 24 cm

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6. Rhombus: all sides = 3 m, height = 3 m

All four sides are 3 m (since it's a rhombus), and height is 3 m.

- Area:
Formula: $ \text{Area} = \text{base} \times \text{height} $
$ 3 \times 3 = 9 $
→ Area = 9 m²

- Perimeter:
All sides equal: $ 4 \times 3 = 12 $
→ Perimeter = 12 m

✔ Answer:
- Area = 9 m²
- Perimeter = 12 m

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✔ Final Answers Summary:

| Shape | Area | Perimeter |
|------|------|-----------|
| 1. Rectangle (15×3 in) | 45 in² | 36 in |
| 2. Right Triangle (6,10,11.7 cm) | 30 cm² | 27.7 cm |
| 3. Rectangle (4×5 ft) | 20 ft² | 18 ft |
| 4. Triangle (5,3,6 m, h=2) | 6 m² | 14 m |
| 5. Parallelogram (9,3, h=2 cm) | 18 cm² | 24 cm |
| 6. Rhombus (side=3 m, h=3 m) | 9 m² | 12 m |

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📝 Number Models (How to Show Work):

For example:

1. Rectangle (15×3)
- Area: $ 15 \times 3 = 45 $
- Perimeter: $ 2(15 + 3) = 2(18) = 36 $

2. Right Triangle
- Area: $ \frac{1}{2} \times 6 \times 10 = 30 $
- Perimeter: $ 6 + 10 + 11.7 = 27.7 $

And so on...

Let me know if you'd like this formatted into a printable answer sheet!