Area of Triangles and Parallelograms Worksheets - Math Monks - Free Printable

Let's solve each problem step by step using the formulas:

Area of a Triangle:

$$
\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}
$$

Area of a Parallelogram:

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

We will go through each figure one by one.

---

Triangles (1–6)

#### 1.
- Base = 12 cm
- Height = 3 cm
$$
\text{Area} = \frac{1}{2} \times 12 \times 3 = 18 \text{ cm}^2
$$

#### 2.
- Base = 8.5 in
- Height = 7 in
$$
\text{Area} = \frac{1}{2} \times 8.5 \times 7 = \frac{1}{2} \times 59.5 = 29.75 \text{ in}^2
$$

#### 3.
- Base = 9 cm
- Height = 4 cm
$$
\text{Area} = \frac{1}{2} \times 9 \times 4 = 18 \text{ cm}^2
$$

#### 4.
- Base = 8.2 cm
- Height = 6.6 cm
$$
\text{Area} = \frac{1}{2} \times 8.2 \times 6.6 = \frac{1}{2} \times 54.12 = 27.06 \text{ cm}^2
$$

#### 5.
- Base = 8.2 in
- Height = 4.4 in
$$
\text{Area} = \frac{1}{2} \times 8.2 \times 4.4 = \frac{1}{2} \times 36.08 = 18.04 \text{ in}^2
$$

#### 6.
- Base = 12 yd
- Height = 9 yd
$$
\text{Area} = \frac{1}{2} \times 12 \times 9 = 54 \text{ yd}^2
$$

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Parallelograms (7–12)

#### 7.
- Base = 8 cm
- Height = 4 cm
$$
\text{Area} = 8 \times 4 = 32 \text{ cm}^2
$$

#### 8.
- Base = 10 cm
- Height = 6 cm
$$
\text{Area} = 10 \times 6 = 60 \text{ cm}^2
$$

#### 9.
- Base = 6 cm
- Height = 3 cm
$$
\text{Area} = 6 \times 3 = 18 \text{ cm}^2
$$

#### 10.
- Base = 16 yd
- Height = 8 yd
$$
\text{Area} = 16 \times 8 = 128 \text{ yd}^2
$$

#### 11.
- Base = 11 m
- Height = 9 m
$$
\text{Area} = 11 \times 9 = 99 \text{ m}^2
$$

#### 12.
- Base = 21.4 in
- Height = 16.6 in
$$
\text{Area} = 21.4 \times 16.6 = 355.24 \text{ in}^2
$$

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✔ Final Answers:

#### Triangles:
1. $ 18 \text{ cm}^2 $
2. $ 29.75 \text{ in}^2 $
3. $ 18 \text{ cm}^2 $
4. $ 27.06 \text{ cm}^2 $
5. $ 18.04 \text{ in}^2 $
6. $ 54 \text{ yd}^2 $

#### Parallelograms:
7. $ 32 \text{ cm}^2 $
8. $ 60 \text{ cm}^2 $
9. $ 18 \text{ cm}^2 $
10. $ 128 \text{ yd}^2 $
11. $ 99 \text{ m}^2 $
12. $ 355.24 \text{ in}^2 $

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🔍 Explanation Summary:

- For triangles, always use $ \frac{1}{2} \times \text{base} \times \text{height} $. The height must be perpendicular to the base.
- For parallelograms, use $ \text{base} \times \text{height} $. Again, height is the perpendicular distance from the base.
- Units are important — keep them consistent and label your answers correctly.

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