Geometry Formulas

We all very well know that Geometry is an aspect of mathematics which we use in our life quite often. It deals with shapes, sizes, figures, properties of space and also with the relative position of the figures. It is the branch of mathematics that helps us in calculating the lengths, width, area, and volumes of various plane figures as well as solid shapes. The history of Geometry relates to ancient times. But, in order to make all the calculations in Geometry, we need to learn all the geometry formulas. So, let’s get started!

Geometry Formulas

What is Geometry?

As stated earlier, Geometry is a branch or division of mathematics that studies the various shapes and sizes along with their area and volume. We can divide Geometry into two different parts for better understanding, viz., Plane Geometry and Solid Geometry. As the name suggests, Plane Geometry deals with the perimeter and area of the plane figures such as squares, rectangles, triangles, circles, trapezium, etc.

However, Solid Geometry is the study of the perimeter, area, and volume of the solid shapes such as a cube, cuboid, cylinders, etc. We can also calculate arc length and radius with the help of these formulas. Let us now study various basic and useful Geometry Formulas.

Basic Geometry Formulas

Though there are many Geometry Formulas, some easy and some complicated, we shall here deal with only the basic ones. Let us begin.

1. The perimeter of a Square:

P = 4a

Where,

P	Perimeter
a	length of the sides of a Square

 

2. Area of a Square:

A = a²

Where,

A	Area
a	Length of the sides of a Square

 

3. Perimeter of a Rectangle:

P = 2(l + b)

Where,

P	Perimeter
l	Length of the side of the rectangle
b	The breadth of the side of the rectangle

 

4. Area of a Rectangle:

A = l × b

Where,

A	Area
l	Length of the side of the rectangle
b	The breadth of the side of the rectangle

 

5. Area of a Triangle:

A = \(\frac{b × h}{2}\)

Where,

A	Area
b	the base of the triangle
h	height of the triangle

 

6. Area of a Trapezoid:

A =  \( \frac{b_1 + b_2}{ 2 } \) h

Where,

A	Area
b1 and b2	bases of the trapezoid
h	height of the trapezoid

 

7. Circumference of a Circle:

\(C = 2 × \pi × r\)

Where,

C	Circumference
r	the radius of the circle

 

8. Area of a Circle:

A = πr²

 Where,

A	Area
r	the radius of the circle

 

9. Surface Area of a Cube:

S = 6a²

 Where,

S	Surface area
a	Length of the sides of a Cube

 

10. Surface Area of a Cylinder:

S = 2 π rh

Where,

S	Surface area
r	The radius of the base of the Cylinder
h	Height of the Cylinder

 

11. The volume of a Cylinder:

V = π r²h

Where,

V	Volume
r	The radius of the base of the Cylinder
h	Height of the Cylinder

 

12. Surface Area of a Cone:

S =πr (r+ \( \sqrt{ h² + r²} \) )

Where,

S	Surface area
r	The radius of the base of the Cone
h	Height of the Cone

 

13. The volume of a Cone:

V= πr² =   \( \frac{h}{r} \)

Where,

V	Volume
r	The radius of the base of the Cone
h	Height of the Cone

 

14. Surface Area of a Sphere:

S = 4 π r² 

Where,

S	Surface area
r	The radius of the sphere

 

15. The volume of a Sphere:

V = \( \frac{4}{3} \)  πr³

Where,

V	Volume
r	The radius of the sphere

Solved Examples

The following examples shall help you understand the Geometry formulas in a better way.

Q. The length and breadth of a wall are 20 ft. and 15 ft. respectively. The owner wants to get it covered with wallpaper. The price of the wallpaper is ₹50 per sq. ft. Find the cost of covering the wall with the wallpaper?

Solution:

Now, let us first understand what is the shape we are talking about and also what do we need to calculate. Looking at the dimensions, we can say that the shape is a rectangle. Also, as we need to cover the whole area of the wall, we need to calculate its area.

Thus,

Area of the wall = l × b

= 20 × 15

= 300 sq. ft.

Cost of wallpaper = Area of the wall × Cost per sq. ft.

= 300 × 50

=  ₹ 15000