Triangles are three-sided closed figures. Finding their area and understanding their properties is crucial for SSC CGL success. This topic appears in 2-3 questions per paper. Core Concept: Triangle area measures the space inside the triangle. Properties tell us relationships between sides and angles.
Sum of all angles = 180°
Sum of any two sides > third side
Exterior angle = sum of two opposite interior angles
In right triangle: a² + b² = c² (Pythagoras theorem)
Area depends on base and height OR three sides OR two sides with included angle
SSC loves asking area with given coordinates, Heron's formula problems, and finding missing sides when area is given. Questions often combine area with similarity or congruence.
#1: For right triangles, if sides are in ratio 3:4:5 or 5:12:13 or 8:15:17, instantly recognize them. Area = (1/2) × product of perpendicular sides. Shortcut Trick #2: When three sides are given, check if a² + b² = c². If yes, it's right triangle.
Use simple area formula instead of Heron's.
Use Heron's formula
s = (13+14+15)/2 = 21
Area = √[21(21-13)(21-14)(21-15)]
Area = √[21 × 8 × 7 × 6]
Area = √[7056] = 84 sq units Worked Example 2: Triangle with vertices A(0,0), B(4,0), C(0,3). Find area.
This forms right triangle with base on x-axis
Base = 4 units, Height = 3 units
Area = (1/2) × 4 × 3 = 6 sq units Alternative: Use coordinate formula = (1/2)|x₁(y₂-y₃) + x₂(y₃-y₁) + x₃(y₁-y₂)| Shortcut Trick #3: For coordinate geometry triangles, if vertices have zeros, use simple base × height method instead of coordinate formula.
#1: Students forget to take square root in Heron's formula. They calculate s(s-a)(s-b)(s-c) and stop there. Always remember the square root symbol!
This single mistake costs many students easy marks. Additional Common Mistakes: Confusing perimeter with semi-perimeter in Heron's formula. Using wrong angle in SAS formula. Not checking if given sides can form a triangle before calculating area.
12graded MCQs · easy to hard · full solution & trap analysis