Know about Geometry Formulas

Geometry is a branch of mathematics that deals with shape, size, the relative position of figures, and the properties of shapes. It emerges independently in the number of early cultures as a practical way of dealing with lengths, area and volumes.

Geometry can be divided into two different types: Plane Geometry and Solid Geometry. The Plane Geometry deals with shapes such as circles, triangles, rectangles, square and more. Whereas, the Solid Geometry is concerned in calculating the length, perimeter, area and volume of various geometric figures and shapes. 

The main concern of every student about maths subject is the Geometry Formulas. They are used to calculate the length, perimeter, area and volume of various geometric shapes and figures.  There are many geometric formulas, which are related to height, width, length, radius, perimeter, area, surface area or volume and much more.

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:

Basic Geometry Formulas

Perimeter of a Square = P = 4a Perimeter o fa Square = P = 4a

Where a = Length of the sides of a Square

Perimeter of a Rectangle = P = 2(l+b) Perimeter of aRectangle = P = 2(l+b)

Where, l = Length ; b = Breadth

Area of a Square = A = a2 Area of a Square = A = a2

Where a = Length of the sides of a Square

Area of a Rectangle = A = l×b Area of a Rectangle = A = l×b

Where, l = Length ; b = Breadth

Area of a Triangle = A = b× h2 Area of a Triangle = A = b×h2

Where b = base of the triangle; h = height of the triangle

Area of a Trapezoid = A = (b1+b2) h2 Area of a Trapezoid = A = (b1+b2) h2

Where, b1b1 & b2b2 are the bases of the Trapezoid; h = height of the Trapezoid

Area of a Circle = A = π×r2 Area of a Circle=A=π×r2

Circumference of a Circle=A=2πr Circumference of a Circle=A=2πr

Where, r = Radius of the Circle

Surface Area of a Cube=S=6a2 Surface Area of a Cube=S=6a2

Where, a = Length of the sides of a Cube

Surface Area of a Cylinder=S=2πrh Surface Area of a Cylinder=S=2πrh

Volume of a Cylinder=V=πr2h Volume of a Cylinder=V=πr2h

Where, r = Radius of the base of the Cylinder; h = Height of the Cylinder

Surface Area of a Cone=S=πr(r+h2+r2−−−−−−√) Surface Area of a Cone=S=πr(r+h2+r2)

Volume of a Cone=V=πr2h Volume of a Cone=V=πr2h

Where, r = Radius of the base of the Cone, h = Height of the Cone

Surface Area of a Sphere=S=4πr2 Surface Area of a Sphere=S=4πr2

Volume of a Sphere=V=43πr3 Volume of a Sphere=V=43πr3

Where, r = Radius of the Sphere

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 sq. 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 60m and 90m respectively?

Solution:

To find the area of a rectangular park:

Given: Length of the park = 60m

The breadth of the park = 90m

Using geometry formulas for rectangle,

Area of Rectangle = (Length × Breadth)

= (60 × 90) m2 

= 5400 m2

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