Lesson 4.3: Geometry (Lines, Circles, Triangles, Mensuration)
Geometry is a key part of the Mathematics section for NDA, CDS, and AFCAT exams. It helps aspirants solve problems related to lines, angles, triangles, circles, and mensuration, which are commonly tested in competitive exams.
1. Lines and Angles
-
Basics: Parallel and perpendicular lines, transversal, alternate angles, corresponding angles
-
Angle Properties: Sum of angles in a triangle = 180°, sum of angles in a quadrilateral = 360°
-
Key Formulas:
-
Sum of interior angles of n-sided polygon = (n-2) × 180°
-
Exterior angle = 180° – Interior angle
-
2. Triangles
-
Types: Equilateral, Isosceles, Scalene, Right-angled
-
Pythagoras Theorem: a² + b² = c² (Right-angled triangle)
-
Area Formulas:
-
Area = ½ × base × height
-
Heron’s Formula: √[s(s-a)(s-b)(s-c)], s = (a+b+c)/2
-
3. Circles
-
Basic Properties: Radius, diameter, circumference, chord, tangent, sector, segment
-
Formulas:
-
Circumference = 2πr
-
Area = πr²
-
Length of arc = (θ/360) × 2πr
-
Area of sector = (θ/360) × πr²
-
4. Mensuration
-
2D Shapes: Rectangle, square, triangle, circle, trapezium
-
3D Shapes: Cube, cuboid, sphere, cone, cylinder
-
Formulas:
-
Volume and Surface Area of solids (e.g., Cube = a³, SA = 6a²)
-
Cylinder: Volume = πr²h, SA = 2πr(h+r)
-
Sphere: Volume = 4/3 πr³, SA = 4πr²
-
Exam Tips
-
Memorize basic formulas for area, volume, and perimeter.
-
Practice diagram-based problems carefully.
-
Solve previous year NDA, CDS, AFCAT geometry questions.
-
Focus on speed and accuracy while calculating.