Let see the all triangle types and methods to finding the area of a triangle! here we are going to discuss types of triables by side and angle. We also learn how to find the area of triangle by three most common used methods. Math Tutors at Math make smart are expert to guide and teach these types of problems to the students. Our tutoring services are higly recommended by parents on the trustpilot.
TRIANGLE TYPES
By Sides:
- Equilateral – all 3 sides equal
- Isosceles – 2 sides equal
- Scalene – all sides different
By Angles:
- Acute – all angles < 90°
- Right – one angle = 90°
- Obtuse – one angle > 90°
METHOD 1: Base × Height (Most Common)
Formula: A = ½ × base × height
The height must be perpendicular to the base.
Example: Triangle with base = 10 cm, height = 6 cm
- A = ½ × 10 × 6
- A = 30 cm²
METHOD 2: Heron’s Formula (Using 3 Sides)
here is the solution by Heron’s Formula
Formula: A = √[s(s-a)(s-b)(s-c)]
Where:
- a, b, c = lengths of the three sides
- s = semi-perimeter = (a+b+c)/2
Example: Triangle with sides 5 cm, 6 cm, 7 cm
- s = (5+6+7)/2 = 9
- A = √[9(9-5)(9-6)(9-7)]
- A = √[9 × 4 × 3 × 2]
- A = √216
- A ≈ 14.7 cm²
METHOD 3: Two Sides and Included Angle
Formula: A = ½ × a × b × sin(C)
Where a and b are two sides, C is the angle between them.
Example: Triangle with sides 8 cm, 10 cm, angle between them = 60°
- A = ½ × 8 × 10 × sin(60°)
- A = ½ × 8 × 10 × 0.866
- A = 34.64 cm²