Geometry Formulas

Geometry formulas are used for finding dimensions, perimeter, area, surface area, volume, etc. of the geometric shapes. Geometry is a part of mathematics that deals with the relationships of points, lines, angles, surfaces, solids measurement, and properties. There are two types of geometry: 2D or plane geometry and 3D or solid geometry.

The 2D shapes are flat shapes that have only two dimensions, length, and width as in squares, circles, and triangles, etc. 3D objects are solid objects, that have three dimensions, length, width, and height or depth, as in a cube, cuboid, sphere, cylinder, cone. Let us learn all geometry formulas along with a few solved examples in the upcoming sections.

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 = ½ × base × height
• Area of a Trapezoid = ½ × (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.

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Let us have a look at solved examples to understand the basic geometry formulas.

Solved Examples Using Geometry Formulas

Example 1: 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

Answer: The area of a circle is 1385.44 square units and the circumference of a circle is 131.95 units.

Example 2: What is the area of a rectangular park whose length and breadth are 90 m and 60 m respectively?

Solution:
To find the area of a rectangular park:

Given: Length of the park = 90 m

The breadth of the park = 60 m
Using the geometry formulas for a rectangle,

Area of Rectangle = (Length × Breadth)

= (90 × 60) m²

= 5400 m²

Answer: The area of the rectangular park is 5400 m².

Example 3: 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

Answer: The surface area of the cube is 216 units². The volume of the cube is 216 units³