Geometry Formulas for CBSE Class 6 to 12 — Area, Volume, Perimeter
Geometry formulas cover area and perimeter of all 2D shapes, surface area and volume of all 3D solids, and coordinate geometry formulas. They are tested in CBSE Class 6 through Class 12, JEE Main, and NEET.
Topics Covered on This Page:
- 2D shape formulas: square, rectangle, triangle, circle, parallelogram, trapezium, rhombus
- 3D solid formulas: cube, cuboid, sphere, hemisphere, cylinder, cone
- Coordinate geometry: distance, midpoint, section, slope, area of triangle
- Heron’s formula and the Pythagorean theorem
- Class-wise NCERT chapter reference
What are Geometry Formulas?
Geometry formulas are mathematical expressions used to calculate properties of shapes — such as area, perimeter, surface area, and volume. Plane geometry deals with 2D figures (triangles, circles, polygons), while solid geometry deals with 3D shapes (spheres, cylinders, cones). Coordinate geometry applies algebra to geometric figures using the Cartesian plane. These formulas are covered from NCERT Class 6 through Class 12.
2D Shape Formulas — Area and Perimeter
| Shape | Area | Perimeter | NCERT Class |
|---|---|---|---|
| Square (side a) | \( a^2 \) | \( 4a \) | Class 6, Ch 10 |
| Rectangle (l, b) | \( l \times b \) | \( 2(l + b) \) | Class 6, Ch 10 |
| Triangle (base b, height h) | \( \frac{1}{2} \times b \times h \) | a + b + c | Class 6, Ch 10 |
| Equilateral Triangle (side a) | \( \frac{\sqrt{3}}{4}a^2 \) | \( 3a \) | Class 9, Ch 12 |
| Circle (radius r) | \( \pi r^2 \) | \( 2\pi r \) | Class 10, Ch 12 |
| Semicircle (radius r) | \( \frac{1}{2}\pi r^2 \) | \( \pi r + 2r \) | Class 10, Ch 12 |
| Parallelogram (base b, height h) | \( b \times h \) | \( 2(a+b) \) | Class 9, Ch 9 |
| Trapezium (parallel sides a, b; height h) | \( \frac{1}{2}(a+b)h \) | a + b + c + d | Class 8, Ch 11 |
| Rhombus (diagonals d₁, d₂) | \( \frac{1}{2} d_1 d_2 \) | \( 4a \) | Class 8, Ch 11 |
| Heron’s Formula (sides a, b, c) | \( \sqrt{s(s-a)(s-b)(s-c)} \), \( s = \frac{a+b+c}{2} \) | a + b + c | Class 9, Ch 12 |
3D Solid Formulas — Volume and Surface Area
| Solid | Volume | Total Surface Area | Lateral Surface Area | NCERT Class |
|---|---|---|---|---|
| Cube (side a) | \( a^3 \) | \( 6a^2 \) | \( 4a^2 \) | Class 9, Ch 13 |
| Cuboid (l, b, h) | \( lbh \) | \( 2(lb+bh+hl) \) | \( 2h(l+b) \) | Class 9, Ch 13 |
| Sphere (radius r) | \( \frac{4}{3}\pi r^3 \) | \( 4\pi r^2 \) | \( 4\pi r^2 \) | Class 9, Ch 13 |
| Hemisphere (radius r) | \( \frac{2}{3}\pi r^3 \) | \( 3\pi r^2 \) | \( 2\pi r^2 \) | Class 9, Ch 13 |
| Cylinder (radius r, height h) | \( \pi r^2 h \) | \( 2\pi r(r+h) \) | \( 2\pi rh \) | Class 9, Ch 13 |
| Cone (radius r, height h, slant l) | \( \frac{1}{3}\pi r^2 h \) | \( \pi r(r+l) \) | \( \pi rl \) | Class 9, Ch 13 |
Coordinate Geometry Formulas
| Concept | Formula | NCERT Class |
|---|---|---|
| Distance between two points | \( d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2} \) | Class 10, Ch 7 |
| Midpoint formula | \( M = \left(\frac{x_1+x_2}{2},\,\frac{y_1+y_2}{2}\right) \) | Class 10, Ch 7 |
| Section formula (internal) | \( P = \left(\frac{mx_2+nx_1}{m+n},\,\frac{my_2+ny_1}{m+n}\right) \) | Class 10, Ch 7 |
| Slope of a line | \( m = \frac{y_2 – y_1}{x_2 – x_1} \) | Class 11, Ch 10 |
| Equation of a line (slope-intercept) | \( y = mx + c \) | Class 11, Ch 10 |
| Area of triangle (coordinate) | \( A = \frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)| \) | Class 10, Ch 7 |
| Equation of circle | \( (x-h)^2 + (y-k)^2 = r^2 \) | Class 11, Ch 11 |
All Geometry Formula Articles
For NCERT Maths textbooks (Class 6 to 12), visit ncert.nic.in. For CBSE sample papers, visit cbse.gov.in.