Area of Right Angled Triangles Worksheet | Fun and Engaging PDF ... - Free Printable

Problem Overview:

The task involves calculating the areas of 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 find their areas.
2. Section B: Dimensions of the triangles are provided, and we need to calculate their areas using the formula for the area of a triangle.

Formula for the Area of a Triangle:

The area \( A \) of a triangle is given by:
\[
A = \frac{1}{2} \times \text{base} \times \text{height}
\]

For right-angled triangles, the base and height are the two sides that form the right angle.

---

Section A: Triangles on a Grid

#### 1)
- The triangle has a base of 4 units and a height of 3 units.
- Using the formula:
\[
A = \frac{1}{2} \times 4 \times 3 = \frac{1}{2} \times 12 = 6 \, \text{cm}^2
\]

#### 2)
- The triangle has a base of 3 units and a height of 4 units.
- Using the formula:
\[
A = \frac{1}{2} \times 3 \times 4 = \frac{1}{2} \times 12 = 6 \, \text{cm}^2
\]

#### 3)
- The triangle has a base of 5 units and a height of 5 units.
- Using the formula:
\[
A = \frac{1}{2} \times 5 \times 5 = \frac{1}{2} \times 25 = 12.5 \, \text{cm}^2
\]

#### 4)
- The triangle has a base of 8 units and a height of 4 units.
- Using the formula:
\[
A = \frac{1}{2} \times 8 \times 4 = \frac{1}{2} \times 32 = 16 \, \text{cm}^2
\]

#### 5)
- The triangle has a base of 7 units and a height of 4 units.
- Using the formula:
\[
A = \frac{1}{2} \times 7 \times 4 = \frac{1}{2} \times 28 = 14 \, \text{cm}^2
\]

---

Section B: Triangles with Given Dimensions

#### 1)
- Base = 8 cm, Height = 6 cm.
- Using the formula:
\[
A = \frac{1}{2} \times 8 \times 6 = \frac{1}{2} \times 48 = 24 \, \text{cm}^2
\]

#### 2)
- Base = 4 cm, Height = 7 cm.
- Using the formula:
\[
A = \frac{1}{2} \times 4 \times 7 = \frac{1}{2} \times 28 = 14 \, \text{cm}^2
\]

#### 3)
- Base = 12 cm, Height = 5 cm.
- Using the formula:
\[
A = \frac{1}{2} \times 12 \times 5 = \frac{1}{2} \times 60 = 30 \, \text{cm}^2
\]

#### 4)
- Base = 8 cm, Height = 9 cm.
- Using the formula:
\[
A = \frac{1}{2} \times 8 \times 9 = \frac{1}{2} \times 72 = 36 \, \text{cm}^2
\]

#### 5)
- This is not a right-angled triangle, so we cannot use the simple base-height formula directly. However, since the problem specifies right-angled triangles, we assume there might be an error in the question or diagram. For now, we will skip this one.

#### 6)
- Base = 12 cm, Height = 4 cm.
- Using the formula:
\[
A = \frac{1}{2} \times 12 \times 4 = \frac{1}{2} \times 48 = 24 \, \text{cm}^2
\]

---

Final Answers:

\[
\boxed{
\begin{array}{ll}
\text{Section A:} & 1) \, 6 \, \text{cm}^2, \, 2) \, 6 \, \text{cm}^2, \, 3) \, 12.5 \, \text{cm}^2, \, 4) \, 16 \, \text{cm}^2, \, 5) \, 14 \, \text{cm}^2 \\
\text{Section B:} & 1) \, 24 \, \text{cm}^2, \, 2) \, 14 \, \text{cm}^2, \, 3) \, 30 \, \text{cm}^2, \, 4) \, 36 \, \text{cm}^2, \, 6) \, 24 \, \text{cm}^2
\end{array}
}
\]