how to learn geometry formulas

Last Updated on August 28, 2023

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how to learn geometry formulas


Geometry, dating back to 3000 BC, is that branch of mathematics that helps in giving shape and dimension to the otherwise flat world around us. It is what makes us discover and measure patterns, areas, angles, and sizes of things around us.

Contrary to how we feel about learning it at school, we use it consciously and unconsciously throughout our day. We use it to make mental calculations while we park our bikes, while deciding the dimensions of a painting or a sculpture, and even while shooting for that goal.

It is a part of our curriculum since the early stages and continues through college and even in higher education. Geometry is extensively used in specialized disciplines like engineering, sports, arts, robotics, automotive, astronomy etc. 

While studying geometry hones many foundation skills like reasoning, logical thinking, problem-solving; learning geometrical formulas is very tricky. But this trick does not underscore the importance of learning and knowing formulae and their applications. 

Some formulas are very complex and might seem like abstract shapes from the outer space! The question is how to memorize formulas and remember them for life?

So, here are some few tips –

1. Make Math & Geometry fun and develop a mindset for it

The first and foremost step is to stop  demonizing  geometry and letting go of all the mental baggage of thinking it to be difficult to study. Think of it, as an ally for anything to what you will pursue in your life. Keeping an open mind for geometry will make it seem easier and friendlier.

2. Understand and not cram

You can easily forget what you crammed, but never what you truly understand. Instead of having a myopic focus on the numbers and symbols, try to understand what that particular formula actually solves. Once you have a semblance of a real world issue being solved by a formula, you are unlikely to forget it ever in your life.

3. Be creative

Instead of cramming up a formula, think and devise ways, which interest you and are sure to sustain. 

Visual aids have been proven to be more comprehensible and retentive especially when it comes to remembering and recalling numbers and symbols. You can make Flashcards, Sticky notes & worksheets, watch videos, say them aloud, quiz yourself, and have a friend or teacher recite them with. These are some of the ways, which have been known to help a lot of students. 

Another interesting technique is to use mnemonics- create an interesting story that sequentially involves the formula that you are trying to learn. Recalling the story is an easy way of remembering the formula.

4. Set your goal

Seeing yourself in an important position in the world of mathematics gives positive reinforcement to your drive to learn. 

Whether you are studying or planning to contribute to the greater body of mathematical knowledge, you cannot do without knowing the correct formulae. Students, Mathematicians, and Geometricians actually spend a lot of time in mathematical writing especially research papers. 

Writing research papers helps in developing one’s comprehensive communication and the ability to explain your mathematical ideas and thinking process. Sometimes, it’s difficult to understand when someone says “write me a research paper”; however, for such occasions only, there are many websites that can help you find the right context of writing research papers. 

5. Stay away from distractions

Set aside distraction free learning time. When you are memorizing something to do with numbers and symbols, it is easy to get bored and sway towards distractions. Avoid wasting your time taking too many breaks, surfing the Internet, and texting your friends. 

6. Get some sleep

A lot of students think that cramming for long hours will help them in learning. This statement could not be further away from the truth. Relax your body and mind with eight hours of sleep. It will ease and quicken your learning process. 

7. Exercise

How to remember things easier? Simple. Sport and exercise help in lowering stress and sending oxygen to your brain. Your mental and physical fitness has a direct impact on your learning capabilities especially numbers. A stressed brain learns slowly and does not retain. Walking, jogging, hiking, and yoga are easy ways to get good exercise. These activities also take you away from the monotony of your room or cramped studying space. More sport and you’ll forget that you ever struggled with the question of how to learn maths fast.

Taking deep breaths also helps in lowering overwhelming and negative feelings. 

8. Eat light

Being hungry or thirsty while studying is sure to distract you, and you will have a hard time concentrating. To learn and memorize better, keep eating light snacks like fruits etc. and consuming water at regular intervals. 

So, I hope now you know how to memorize things quickly.  

Apart from the stuff given in this section,  if you need any other stuff in math, please use our google custom search here.

geometry formulas with examples

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.

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:

Geometry formulas

List of Geometry Formulas

Below is the list of various geometry formulas for you according to the geometric shape.

  • 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)(base1+base2) × height

Basic geometry formulas where the mathematical constant π is used are,

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


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

The formula table depicts the geometry formulas used for different 2-D and 3-D shapes:

1. Right TrianglePythagoras Theorem: a2 + b2 = c2Area = ½ abPerimeter = a + b + √(a2 + b2)Where,
c = hypotenuse of a trianglea = altitude of a triangleb = base of a triangle
2. TrianglePerimeter, P = a + b + cArea, A = ½ bhHeight, h = 2(A/b)Where,a,b,c are the sides of a triangle.
3. RectanglePerimeter = 2(l + w)Area = lwDiagonal, d = √(l2 + w2)Where,l = length of a rectanglew = width of a rectangle
4.ParallelogramPerimeter, P = 2(a + b)Area, A = bhHeight, h = A/bBase, b = A/hWhere,a and b are the sides of a parallelogramh = height of a parallelogram
5. TrapeziumArea, A = ½(a + b)hHeight, h = 2A/(a + b)Base, b = 2(A/h) – aWhere,a and b are the parallel sidesh = distance between two parallel sides
6. CircleCircumference = 2πrArea = πr2Diameter = 2rWhere,r = radius of a circle
7. SquarePerimeter, P = 4aArea, A = a2Diagonal, d = a√2Side, a = √A = d/2√2Where,a = side of a square
8. ArcArc Length, L = rθArea, A = ½r2θHere, θ is the central angle is radians.Where,r = radius 
9. CubeArea, A = 6a2Volume, V = a3 Edge, a = VSpace diagonal = a√3Where,a = side of a cube
10. CuboidSurface Area, A = 2(lb + bh + hl)Volume, V = lbh Space diagonal, d = √( l2 + b2 +h2)Where,l= lengthb= breathh= height
11. CylinderTotal Surface Area, A = 2πrh + 2πr2Curved Surface Area, Ac = 2πrhVolume, V = πr2hBase Area, Ab = πr2Radius, r = √(V/πh)Where,r= radius of a cylinderh= height of a cylinder
12. ConeTotal Surface Area, A = πr(r+l) = πr[r+√(h2+r2)]Curved Surface Area, Ac = πrlVolume, V = ⅓πr2hSlant Height, l = √(h2+r2)Base Area, Ab = πr2Where,r= radius of a coneh= height of a conel = slant height
13. SphereSurface Area, A = 4πr2Volume, V = ⁴⁄₃πr3Diameter = 2rWhere,r= radius of a sphere

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Let’s have a look at solved examples to understand geometry Formulas better.

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?


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×r
= 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?

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.

Example 3: Using geometry formulas of the cube, calculate the surface area and volume of a cube whose edge is 6 units respectively?

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

FAQ’s on Geometry Formulas

What Are the Geometry Formulas of a Cuboid?

What Are the Geometry Formulas of a Rectangle?

What Are the Geometry Formulas of a Cone?

What Are the Geometry Formulas of a Circle?

geometry formulas for class 10

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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.

Some geometric formulas are rather complicated and few you might hardly ever seen them, however, there are some basic formulas which are used in our daily life to calculate the length, space and so on.

Geometry Formulas from Class 8 to Class 12
Geometry Formulas For Class 12
Geometry Formulas For Class 11
Geometry Formulas For Class 10
Geometry Formulas For Class 9
Geometry Formulas For Class 8

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

More topics in Geometry Formulas
Angle FormulaArea Formulas
Asymptote FormulaAxis of Symmetry Formula
Circle FormulaCone Formula
Cyclic Quadrilateral FormulaEllipse Formula
Equation of a Line FormulaHexagon Formula
Midpoint FormulaOctagon Formula
Parabola FormulaParallelogram Formula
Perimeter FormulasPolygon Formula
Prism FormulaRate of Change Formula
Rectangle FormulaRotation Formula
Slope FormulaSphere formula
Square FormulaSurface Area Formulas
Tangent Line FormulaTangential Quadrilateral Formula
The Distance FormulaTriangle Formula
Vertex FormulaVolume Formulas
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