Area of Non-Right Angled Triangles Worksheet | PDF printable ... - Free Printable

Problem Overview:

The task involves calculating the areas of non-right-angled triangles. The worksheet is divided into two sections:

1. Section A: Triangles are drawn on a 1 cm squared grid, and we need to estimate their areas.
2. Section B: Triangles are provided with dimensions (base and height), and we need to calculate their areas using the formula for the area of a triangle:
\[
\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}
\]

---

Solution:

#### Section A: Estimating Areas on a Grid

For each triangle in Section A, we will count the number of full squares and partial squares to estimate the area.

1. Triangle 1:
- Base: 6 cm
- Height: 5 cm
- Area: \(\frac{1}{2} \times 6 \times 5 = 15 \, \text{cm}^2\)

2. Triangle 2:
- Base: 6 cm
- Height: 4 cm
- Area: \(\frac{1}{2} \times 6 \times 4 = 12 \, \text{cm}^2\)

3. Triangle 3:
- Base: 8 cm
- Height: 6 cm
- Area: \(\frac{1}{2} \times 8 \times 6 = 24 \, \text{cm}^2\)

4. Triangle 4:
- Base: 9 cm
- Height: 7 cm
- Area: \(\frac{1}{2} \times 9 \times 7 = 31.5 \, \text{cm}^2\)

5. Triangle 5:
- Base: 10 cm
- Height: 6 cm
- Area: \(\frac{1}{2} \times 10 \times 6 = 30 \, \text{cm}^2\)

---

#### Section B: Calculating Areas Using Dimensions

For each triangle in Section B, we will use the formula:
\[
\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}
\]

1. Triangle 1:
- Base: 10 cm
- Height: 7 cm
- Area: \(\frac{1}{2} \times 10 \times 7 = 35 \, \text{cm}^2\)

2. Triangle 2:
- Base: 4 cm
- Height: 12 cm
- Area: \(\frac{1}{2} \times 4 \times 12 = 24 \, \text{cm}^2\)

3. Triangle 3:
- Base: 14 cm
- Height: 8 cm
- Area: \(\frac{1}{2} \times 14 \times 8 = 56 \, \text{cm}^2\)

4. Triangle 4:
- Base: 2 cm
- Height: 7 cm
- Area: \(\frac{1}{2} \times 2 \times 7 = 7 \, \text{cm}^2\)

5. Triangle 5:
- Base: 20 cm
- Height: 6 cm
- Area: \(\frac{1}{2} \times 20 \times 6 = 60 \, \text{cm}^2\)

6. Triangle 6:
- Base: 5 cm
- Height: 8 cm
- Area: \(\frac{1}{2} \times 5 \times 8 = 20 \, \text{cm}^2\)

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Final Answers:

#### Section A
1. \(15 \, \text{cm}^2\)
2. \(12 \, \text{cm}^2\)
3. \(24 \, \text{cm}^2\)
4. \(31.5 \, \text{cm}^2\)
5. \(30 \, \text{cm}^2\)

#### Section B
1. \(35 \, \text{cm}^2\)
2. \(24 \, \text{cm}^2\)
3. \(56 \, \text{cm}^2\)
4. \(7 \, \text{cm}^2\)
5. \(60 \, \text{cm}^2\)
6. \(20 \, \text{cm}^2\)

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Boxed Final Answer:

\[
\boxed{
\begin{array}{ll}
\text{Section A:} & 15, 12, 24, 31.5, 30 \\
\text{Section B:} & 35, 24, 56, 7, 60, 20
\end{array}
}
\]