Triangle area and perimeter calculation worksheet with nine problems.

I'll solve each triangle problem step by step, calculating the area, perimeter, and identifying the type.

Triangle 1:
- Given: a = 4.27 ft, b = 9.21 ft, c = 9.8 ft, h = 4 ft
- Area = (1/2) × base × height = (1/2) × 9.8 × 4 = 19.6 ft²
- Perimeter = a + b + c = 4.27 + 9.21 + 9.8 = 23.28 ft
- Type: Scalene (all sides different lengths)

Triangle 2:
- Given: a = 7.4 inches, b = 4.8 inches, c = 8.82 inches (right triangle with right angle between a and b)
- Area = (1/2) × 7.4 × 4.8 = 17.76 in²
- Perimeter = 7.4 + 4.8 + 8.82 = 21.02 in
- Type: Right scalene (has right angle, all sides different)

Triangle 3:
- Given: a = 5.71 mm, b = 8.49 mm, c = 8.4 mm, h = 5.4 mm
- Area = (1/2) × 8.4 × 5.4 = 22.68 mm²
- Perimeter = 5.71 + 8.49 + 8.4 = 22.6 mm
- Type: Scalene (all sides different)

Triangle 4:
- Given: s = 5.9 yds (equilateral triangle - all sides equal to s)
- For equilateral triangle, we need height first: h = (√3/2) × s = 0.866 × 5.9 ≈ 5.11 yds
- Area = (1/2) × 5.9 × 5.11 ≈ 15.07 yd²
- Or using formula: Area = (√3/4) × s² = 0.433 × 34.81 ≈ 15.07 yd²
- Perimeter = 3 × 5.9 = 17.7 yds
- Type: Equilateral (all sides equal)

Triangle 5:
- Given: a = 8.6 ft, b = 4.3 ft, c = 9.62 ft (right triangle)
- Area = (1/2) × 8.6 × 4.3 = 18.49 ft²
- Perimeter = 8.6 + 4.3 + 9.62 = 22.52 ft
- Type: Right scalene

Triangle 6:
- Given: a = 4.5 cm, b = 6.4 cm (isosceles triangle with two sides = b)
- Third side = a = 4.5 cm
- Need height: Using Pythagorean theorem, h = (6.4² - 2.25²) = √(40.96 - 5.0625) = √35.8975 ≈ 5.99 cm
- Area = (1/2) × 4.5 × 5.99 ≈ 13.48 cm²
- Perimeter = 4.5 + 6.4 + 6.4 = 17.3 cm
- Type: Isosceles (two sides equal)

Triangle 7:
- Given: a = 6.33 yds, b = 8.16 yds, c = 8.6 yds, h = 5.7 yds
- Area = (1/2) × 8.6 × 5.7 = 24.51 yd²
- Perimeter = 6.33 + 8.16 + 8.6 = 23.09 yds
- Type: Scalene (all sides different)

Triangle 8:
- Given: a = 8.2 cm, b = 5 cm, c = 9.6 cm (right triangle)
- Area = (1/2) × 8.2 × 5 = 20.5 cm²
- Perimeter = 8.2 + 5 + 9.6 = 22.8 cm
- Type: Right scalene

Triangle 9:
- Given: a = 4 inches, b = 6.7 inches (isosceles with two sides = b)
- Third side = a = 4 inches
- Height: h = √(6.7² - 2²) = √(44.89 - 4) = √40.89 ≈ 6.39 inches
- Area = (1/2) × 4 × 6.39 ≈ 12.78 in²
- Perimeter = 4 + 6.7 + 6.7 = 17.4 in
- Type: Isosceles (two sides equal)

Final Answer:

1) Area: 19.6 ft², Perimeter: 23.28 ft, Type: Scalene

2) Area: 17.76 in², Perimeter: 21.02 in, Type: Right scalene

3) Area: 22.68 mm², Perimeter: 22.6 mm, Type: Scalene

4) Area: 15.07 yd², Perimeter: 17.7 yds, Type: Equilateral

5) Area: 18.49 ft², Perimeter: 22.52 ft, Type: Right scalene

6) Area: 13.48 cm², Perimeter: 17.3 cm, Type: Isosceles

7) Area: 24.51 yd², Perimeter: 23.09 yds, Type: Scalene

8) Area: 20.5 cm², Perimeter: 22.8 cm, Type: Right scalene

9) Area: 12.78 in², Perimeter: 17.4 in, Type: Isosceles