Find the area of the triangle in which
Q(i) base = 42 cm and height = 25 cm
(ii) base = 16.8 m and height = 75 cm
(iii) base = 8 dm and height = 35 cm.

Answer

To find the area of the triangles given in the question, we will use the formula for the area of a triangle:

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

Let's solve each part step by step.

### (i) Base = 42 cm and Height = 25 cm

1. **Identify the base and height**:
- Base = 42 cm
- Height = 25 cm

2. **Substitute the values into the area formula**:
\[ \text{Area} = \frac{1}{2} \times 42 \times 25 \]

3. **Calculate the multiplication**:
\[ 42 \times 25 = 1050 \]

4. **Divide by 2**:
\[ \text{Area} = \frac{1050}{2} = 525 \text{ cm}^2 \]

### (ii) Base = 16.8 m and Height = 75 cm

1. **Convert the height from cm to m**:
- Height in meters = \( \frac{75}{100} = 0.75 \) m

2. **Identify the base and height**:
- Base = 16.8 m
- Height = 0.75 m

3. **Substitute the values into the area formula**:
\[ \text{Area} = \frac{1}{2} \times 16.8 \times 0.75 \]

4. **Calculate the multiplication**:
\[ 16.8 \times 0.75 = 12.6 \]

5. **Divide by 2**:
\[ \text{Area} = \frac{12.6}{2} = 6.3 \text{ m}^2 \]

### (iii) Base = 8 dm and Height = 35 cm

1. **Convert the base from dm to cm**:
- Base in cm = \( 8 \times 10 = 80 \) cm

2. **Identify the base and height**:
- Base = 80 cm
- Height = 35 cm

3. **Substitute the values into the area formula**:
\[ \text{Area} = \frac{1}{2} \times 80 \times 35 \]

4. **Calculate the multiplication**:
\[ 80 \times 35 = 2800 \]

5. **Divide by 2**:
\[ \text{Area} = \frac{2800}{2} = 1400 \text{ cm}^2 \]

### Summary of Areas:
- (i) Area = 525 cm²
- (ii) Area = 6.3 m²
- (iii) Area = 1400 cm²