Important Formula: Geometry | Mathematics for RRB NTPC / ASM - RRB NTPC/ASM/CA/TA PDF Download

Geometry formulas are essential for calculating dimensions, perimeter, area, surface area, volume, and other properties of geometric figures. Geometry, a branch of mathematics, focuses on the relationships between points, lines, angles, surfaces, and solids, as well as their measurements and characteristics. 
Geometry can be divided into two main categories: 2D or plane geometry and 3D or solid geometry. 
2D shapes, such as squares, circles, and triangles, are flat figures with only two dimensions: length and width. In contrast, 3D shapes like cubes, cuboids, spheres, cylinders, and cones are solid figures with three dimensions: length, width, and height or depth. The following sections will explore various geometry formulas along with solved examples for better understanding.

What are Geometry Formulas?

The formulas used for finding dimensions, perimeter, area, surface area, volume, etc. of 2D and 3D geometric shapes are known as geometry formulas. 2D shapes consist of flat shapes like squares, circles, and triangles, etc., and cube, cuboid, sphere, cylinder, cone, etc are some examples of 3D shapes. The basic geometry formulas are given as follows:

Basic Geometry Formulas

Let us see the list of all Basic Geometry Formulas here.

2D Geometry Formulas

Here is the list of various 2d geometry formulas according to the geometric shape. It also includes a few formulas where the mathematical constant π(pi) is used.

• Perimeter of a Square = 4(Side)
• Perimeter of a Rectangle = 2(Length + Breadth)
• Area of a Square = Side²
• Area of a Rectangle = Length × Breadth
• Area of a Triangle = 1/2 × base × height
• Area of a Trapezoid = 1/2 × (base₁ + base₂) × height
• Area of a Circle = A = π×r²
• Circumference of a Circle = 2πr

3D Geometry Formulas

The basic 3D geometry formulas are given as follows. It should be noted that the following formulas have used the mathematical constant π(pi)

• The curved surface area of a Cylinder = 2πrh
• Total surface area of a Cylinder = 2πr(r + h)
• Volume of a Cylinder = V = πr²h
• The curved surface area of a cone = πrl
• Total surface area of a cone = πr(r+l) = πr[r+√(h²+r²)]
• Volume of a Cone = V = ⅓×πr²h
• Surface Area of a Sphere = S = 4πr²
• Volume of a Sphere = V = 4/3×πr³

where,

• r = Radius;
• h = Height. and,
• l = Slant height

The formula table depicts the 2D geometry formulas and 3D geometry formulas.

Solved Examples

Example 1: Using geometry formulas of the cube, calculate the surface area and volume of a cube whose edge is 6 units.
Solution: To Find: The surface area and volume of a cube whose edge is 6 units
Using geometry formulas of cube,
Surface area of cube is = A = 6a²
A = 6 (6)²
A = 6 × 36 = 216 units²
Volume of a cube, V = a³
V = (6)³
V = 216 units³ 

Example 2: Calculate the circumference and the area and of a circle by using geometry formulas if the radius of the circle is 21 units.
Solution: To find the area and the circumference of the circle.
Given: Radius of a circle = 21 units
Using geometry formulas for circle,
Area of circle = π × r²
= 3.142857 × 21²
= 1385.44
Now for the circumference of the circle,
Using geometry formulas for circle,
Circumference of a Circle = 2πr
= 2(3.142857)(21)
= 131.95