Area of Triangles Worksheets - Free Printable

To solve the problem of finding the areas of the triangles in the image, we need to use the formula for the area of a triangle:

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

Step-by-Step Solution:

#### 1. Identify the base and height for each triangle:
- The base is the length of one side of the triangle.
- The height is the perpendicular distance from the base to the opposite vertex.

#### 2. Apply the formula for each triangle:
- For each triangle, substitute the given base and height into the formula:
\[
\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}
\]

#### 3. Calculate the area for each triangle:
Let's assume the dimensions provided in the image are as follows (since the actual image is not visible, I will create hypothetical examples):

---

Hypothetical Example Calculations:

#### Triangle 1:
- Base = 6 units
- Height = 4 units
\[
\text{Area} = \frac{1}{2} \times 6 \times 4 = \frac{1}{2} \times 24 = 12 \text{ square units}
\]

#### Triangle 2:
- Base = 8 units
- Height = 5 units
\[
\text{Area} = \frac{1}{2} \times 8 \times 5 = \frac{1}{2} \times 40 = 20 \text{ square units}
\]

#### Triangle 3:
- Base = 10 units
- Height = 3 units
\[
\text{Area} = \frac{1}{2} \times 10 \times 3 = \frac{1}{2} \times 30 = 15 \text{ square units}
\]

#### Triangle 4:
- Base = 7 units
- Height = 6 units
\[
\text{Area} = \frac{1}{2} \times 7 \times 6 = \frac{1}{2} \times 42 = 21 \text{ square units}
\]

#### Triangle 5:
- Base = 9 units
- Height = 4 units
\[
\text{Area} = \frac{1}{2} \times 9 \times 4 = \frac{1}{2} \times 36 = 18 \text{ square units}
\]

#### Triangle 6:
- Base = 5 units
- Height = 7 units
\[
\text{Area} = \frac{1}{2} \times 5 \times 7 = \frac{1}{2} \times 35 = 17.5 \text{ square units}
\]

#### Triangle 7:
- Base = 12 units
- Height = 3 units
\[
\text{Area} = \frac{1}{2} \times 12 \times 3 = \frac{1}{2} \times 36 = 18 \text{ square units}
\]

#### Triangle 8:
- Base = 11 units
- Height = 5 units
\[
\text{Area} = \frac{1}{2} \times 11 \times 5 = \frac{1}{2} \times 55 = 27.5 \text{ square units}
\]

---

Final Answer:

Based on the hypothetical calculations, the areas of the triangles would be:

\[
\boxed{12, 20, 15, 21, 18, 17.5, 18, 27.5}
\]

If you provide the actual dimensions from the image, I can recalculate the areas accurately. Otherwise, this approach should help you solve similar problems.