1. 2D Plane Figures: Triangles & Quadrilaterals

Right triangle: Area = (1/2) × base × height. Equilateral triangle of side a: Area = (√3 / 4) a², Height = (√3 / 2) a. Scalene triangle (Heron's Formula): Area = √[s(s - a)(s - b)(s - c)], where semi-perimeter s = (a + b + c)/2. Parallelogram: Area = base × height. Rhombus with diagonals d1, d2: Area = (1/2) × d1 × d2, Side = (1/2)√(d1² + d2²). Trapezium: Area = (1/2) × (sum of parallel sides) × height.

2. Circles, Sectors & Annulus (Rings)

Circle of radius r: Perimeter (Circumference) = 2πr, Area = πr². Semi-circle: Perimeter = πr + 2r = r(π + 2), Area = (1/2)πr². Circular Ring (between radii R and r): Area = π(R² - r²). Sector of circle with central angle θ (in degrees): Arc length l = (θ / 360°) × 2πr; Sector Area = (θ / 360°) × πr² = (1/2) × l × r.

3. 3D Solids: Cuboid & Cube

Cuboid (dimensions l, w, h): Volume = l × w × h; Total Surface Area (TSA) = 2(lw + wh + hl); Lateral Surface Area (LSA / Area of 4 walls) = 2h(l + w); Body Diagonal = √(l² + w² + h²). Cube of side a: Volume = a³; TSA = 6a²; LSA = 4a²; Body Diagonal = a√3.

4. 3D Curved Solids: Cylinder, Cone & Frustum

Right Circular Cylinder (radius r, height h): Volume = πr²h; Curved Surface Area (CSA) = 2πrh; TSA = 2πr(h + r). Right Circular Cone (radius r, height h, slant height l = √(r² + h²)): Volume = (1/3)πr²h; CSA = πrl; TSA = πr(l + r). Frustum of Cone (radii R and r, height h, slant height L = √[h² + (R - r)²]): Volume = (1/3)πh(R² + r² + Rr); CSA = π(R + r)L; TSA = π[(R + r)L + R² + r²].

5. Spheres & Hemispheres

Sphere of radius r: Volume = (4/3)πr³; Surface Area = 4πr² (for a sphere, CSA = TSA). Solid Hemisphere: Volume = (2/3)πr³; Curved Surface Area = 2πr²; Total Surface Area = 3πr² (adding circular flat base). Spherical Shell (outer radius R, inner radius r): Volume of material = (4/3)π(R³ - r³).