Area of Triangles Worksheets - Free Printable

I'll solve each triangle area problem step by step using the formula for the area of a triangle:

Area = (base × height) ÷ 2

Let me go through each triangle:

1. Triangle 1: Base = 4.6 ft, Height = 7.1 ft
- Area = (4.6 × 7.1) ÷ 2 = 32.66 ÷ 2 = 16.33 ft²

2. Triangle 2: Base = 13.3 m, Height = 14.2 m
- Area = (13.3 × 14.2) ÷ 2 = 188.86 ÷ 2 = 94.43 m²

3. Triangle 3: Base = 14.2 mm, Height = 10.3 mm
- Area = (14.2 × 10.3) ÷ 2 = 145.66 ÷ 2 = 72.83 mm²

4. Triangle 4: Base = 5.2 mm, Height = 7.5 mm
- Area = (5.2 × 7.5) ÷ 2 = 39 ÷ 2 = 19.5 mm²

5. Triangle 5: This is an equilateral triangle with all sides 12.7 ft
- For equilateral triangles: Area = (s² × √3) ÷ 4 where s is side length
- Area = (12.7² × √3) ÷ 4 = (161.29 × 1.732) ÷ 4 ≈ 280.4 ÷ 4 = 70.1 ft²
- Alternatively, if we use base and height: Area = (12.7 × 12.7) ÷ 2 = 161.29 ÷ 2 = 80.645 ft²
- Wait, this doesn't match. Let me recalculate:
- Actually, since it's labeled as having height 12.7 ft, I'll use: Area = (12.7 × 12.7) ÷ 2 = 80.645 ft²

6. Triangle 6: Base = 12.5 cm, Height = 7.8 cm
- Area = (12.5 × 7.8) ÷ 2 = 97.5 ÷ 2 = 48.75 cm²

7. Triangle 7: This appears to be an equilateral triangle with all sides 14.8 mm
- Area = (14.8² × √3) ÷ 4 = (219.04 × 1.732) ÷ 4 ≈ 379.3 ÷ 4 = 94.83 mm²

8. Triangle 8: Base = 6.5 in, Height = 5.7 in
- Area = (6.5 × 5.7) ÷ 2 = 37.05 ÷ 2 = 18.525 in²

9. Triangle 9: Base = 10 mm, Height = 7.6 mm
- Area = (10 × 7.6) ÷ 2 = 76 ÷ 2 = 38 mm²

10. Triangle 10: This appears to be an equilateral triangle with all sides 6.7 mm
- Area = (6.7² × √3) ÷ 4 = (44.89 × 1.732) ÷ 4 ≈ 77.76 ÷ 4 = 19.44 mm²

Final Answers:
1. 16.33 ft²
2. 94.43 m²
3. 72.83 mm²
4. 19.5 mm²
5. 80.645 ft²
6. 48.75 cm²
7. 94.83 mm²
8. 18.525 in²
9. 38 mm²
10. 19.44 mm²

The key concept here is that for any triangle, you need the base and the corresponding height (the perpendicular distance from the base to the opposite vertex). The formula is always (base × height) ÷ 2.