How to Find the Area of a Parallelogram - Maths with Mum - Free Printable

To solve the problem of finding the area of a parallelogram, we use the formula:

$$
\text{Area} = \text{base} \times \text{height}
$$

> Important: The height must be the perpendicular distance from the base to the opposite side, not the slant side.

Let’s go through each parallelogram one by one.

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a)

- Base = 6 cm
- Height = 4 cm (perpendicular height shown)
$$
\text{Area} = 6 \times 4 = 24 \text{ cm}^2
$$

✔ Answer: 24 cm²

---

b)

- Base = 5 km
- Height = 9 km (perpendicular height shown)
$$
\text{Area} = 5 \times 9 = 45 \text{ km}^2
$$

✔ Answer: 45 km²

---

c)

- Base = 8 mm
- Height = 7 mm (perpendicular height shown)
$$
\text{Area} = 8 \times 7 = 56 \text{ mm}^2
$$

✔ Answer: 56 mm²

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d)

- Base = 12 cm
- Height = 4 cm (perpendicular height shown)
$$
\text{Area} = 12 \times 4 = 48 \text{ cm}^2
$$

✔ Answer: 48 cm²

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e)

- Base = 11 m
- Height = 10 m (perpendicular height shown)
> Note: The 3 m is a side, not the height. But the height is clearly marked as 10 m perpendicular to the base.
$$
\text{Area} = 11 \times 10 = 110 \text{ m}^2
$$

✔ Answer: 110 m²

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f)

This one is a bit trickier — it's a parallelogram with sides labeled, but we need to identify the base and height.

- One side is 9 cm (vertical), and another is 12 cm (slanted).
- The height is given as 8 cm, which is the perpendicular distance from the base to the top side.
- The base is 12 cm (horizontal side), and the height is 8 cm (shown as perpendicular).

So:
$$
\text{Area} = 12 \times 8 = 96 \text{ cm}^2
$$

> Note: The 9 cm is a side, not the height. The height is 8 cm, as indicated by the right-angle symbol.

✔ Answer: 96 cm²

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✔ Final Answers:

| Parallelogram | Area |
|---------------|------|
| a) | 24 cm² |
| b) | 45 km² |
| c) | 56 mm² |
| d) | 48 cm² |
| e) | 110 m² |
| f) | 96 cm² |

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🔍 Summary:

Always remember:
- Use base × height, where height is perpendicular to the base.
- Don’t confuse the slant side with the height unless it's explicitly perpendicular.

Let me know if you'd like a visual explanation or help understanding any specific part!