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The image contains three different questions involving triangles:

### Question 2
**Q2:** Find the area of each of the triangles shown below. Each base and height is measured in decimal places.
  
- First Triangle:
  - Base: 2.9 cm
  - Height: 1.5 cm
- Second Triangle:
  - Base: 4.2 cm
  - Height: 2.8 cm
- Third Triangle:
  - Base: 5.3 cm
  - Height: 4.1 cm

**Formula to use:** Area of a triangle = \(\frac{1}{2} \times \text{Base} \times \text{Height}\)

### Question 3
**Q3:** Find the area of each of the triangles shown below. Each base and height is measured in decimal places.

- First Triangle:
  - Base: 6.7 cm
  - Height: 3.4 cm
- Second Triangle:
  - Base: 5.1 cm
  - Height: 2.5 cm
- Third Triangle:
  - Base: 8.6 cm
  - Height: 4.5 cm

**Formula to use:** Area of a triangle = \(\frac{1}{2} \times \text{Base} \times \text{Height}\)

### Question 4
**Q4:** Find the area of each of the triangles below in square units. Find the missing area by using either \( \frac{1}{2} \times \text{base} \times \text{height} \) or \( \text{Area} = \frac{ab \sin(C)}{2} \).

- First Triangle:
  - Side a: 6.3 cm
  - Side b: 9.2 cm
  - Angle C: 51°
- Second Triangle:
  - Side a: 8.1 cm
  - Side b: 10.4 cm
  - Angle C: 37°

Let's solve each problem step-by-step. 

### Solutions

1. **Q2 - Area Calculations:**
   - **First Triangle:** Area = \(\frac{1}{2} \times 2.9 \times 1.5\) cm²
   - **Second Triangle:** Area = \(\frac{1}{2} \times 4.2 \times 2.8\) cm²
   - **Third Triangle:** Area = \(\frac{1}{2} \times 5.3 \times 4.1\) cm²

2. **Q3 - Area Calculations:**
   - **First Triangle:** Area = \(\frac{1}{2} \times 6.7 \times 3.4\) cm²
   - **Second Triangle:** Area = \(\frac{1}{2} \times 5.1 \times 2.5\) cm²
   - **Third Triangle:** Area = \(\frac{1}{2} \times 8.6 \times 4.5\) cm²

3. **Q4 - Area Calculations using Trigonometric Formula:**
   - **First Triangle:** Area = \(\frac{1}{2} \times 6.3 \times 9.2 \times \sin(51^\circ)\)
   - **Second Triangle:** Area = \(\frac{1}{2} \times 8.1 \times 10.4 \times \sin(37^\circ)\)

Let's perform these calculations:Here are the calculated areas for each triangle:

### Q2 - Triangle Areas
1. **First Triangle:** Area = 2.17 cm²
2. **Second Triangle:** Area = 5.88 cm²
3. **Third Triangle:** Area = 10.86 cm²

### Q3 - Triangle Areas
1. **First Triangle:** Area = 11.39 cm²
2. **Second Triangle:** Area = 6.38 cm²
3. **Third Triangle:** Area = 19.35 cm²

### Q4 - Triangle Areas using Trigonometric Formula
1. **First Triangle:** Area = 22.52 cm²
2. **Second Triangle:** Area = 25.35 cm²

Would you like any further details on these calculations, or do you have any other questions?

### Related Questions
1. How do you calculate the area of a triangle using the sine formula?
2. What are the differences between calculating the area of a triangle with the base-height method versus using trigonometry?
3. How do you convert degrees to radians when using trigonometric functions?
4. How does changing one angle affect the area of a triangle?
5. Can the sine formula be used for all types of triangles?

### Tip:
Always double-check the angle measurement mode (degrees vs. radians) when using trigonometric functions on a calculator or in programming to avoid errors in calculations.

Find the area of each of the triangles shown below using the given measurements and formulas.

Explore the step-by-step solutions for calculating the area of various triangles using both the base-height method and trigonometric formulas. This guide covers essential geometry and trigonometry concepts suitable for high school students.

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