What Are the Geometry Formulas?

The 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. 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 geometry formulas along with a few solved examples in the upcoming sections.

Here is a list of several most important geometry formulas that you use for solving various problems.

Basic Geometry Formulas

• Perimeter of a Square = P = 4a

Where a = Length of the sides of a Square

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

Where, l = Length ; b = Breadth

• Area of a Square = A = a2

Where a = Length of the sides of a Square

• Area of a Rectangle = A = l×b

Where, l = Length ; b = Breadth

• Area of a Triangle = A = ½×b×h

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

• Area of a Trapezoid = A = ½×(b1 + b2)×h

Where b1 & b2 are the bases of the Trapezoid; h = height of the Trapezoid

• Area of a Circle = A = π×r2
• Circumference of a Circle = A = 2πr

Where, r = Radius of the Circle

• Surface Area of a Cube = S = 6a2

Where, a = Length of the sides of a Cube

• Curved surface area of a Cylinder  = 2πrh
• Total surface area of a Cylinder = 2πr(r + h)
• Volume of a Cylinder = V = πr2h

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

• 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

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

• Surface Area of a Sphere = S = 4πr2
• Volume of a Sphere = V = 4/3×πr3

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