Geometry Formulas
Have you ever gotten stuck while solving geometry questions? This is a common problem with students, especially those who find geometry formulas difficult. These formulas help you find the required dimensions of geometric shapes easily.
In this blog, you will learn about all geometric formulas of 2d and 3d shapes with solved examples.
What are Geometry Formulas
Geometry formulas are those formulas used to find the dimensions, surface area, area, perimeter, volume, circumference, and other parameters of plane and solid geometric shapes.
In simple terms, Geometry formulas are mathematical rules to find the parameters of various figures. These formulas are used in mathematics, physics, and everyday problem-solving. They cover everything from simple lengths to complex spatial measurements.
What are Geometrical Shapes
Geometric shapes are figures or forms defined by a specific set of mathematical properties and dimensions, such as points, lines, sides, angles, and curves.
There are two types of geometrical shapes, plane shapes and solid shapes. The plane shapes are called 2D shapes, and the solids are known as 3D shapes.
The primary difference is the number of dimensions and the physical space the shapes occupy.
Plane (2D) Geometry Formulas
Plane geometry formulas are used to find the parameters of two-dimensional shapes like triangles, quadrilaterals, and circles. You will learn all geometry formulas for 2D shapes. Some of the formulas also contain a mathematical constant called pi.
Square Geometry Formulas
A square is a flat, four-sided shape where all sides are equal in length, and all four internal angles are right angles (90 degrees).
The geometric formulas of a square are given as;
Area of Square = A = a^2
perimeter of Square=4a
Geometry Formulas for Rectangle
A rectangle is a flat, four-sided shape with four right (90-degree) angles. Its opposite sides are equal in length and parallel, making it a type of parallelogram.
The rectangle geometry formulas are;
Perimeter of a Rectangle = 2(Length + Breadth)
Area of a Rectangle = Length × Breadth
Triangle Geometry Formulas
A triangle is a fundamental two-dimensional geometric shape. It is a closed polygon with three sides, three angles, and three vertices. It is the simplest possible polygon, formed by connecting three non-collinear points in a plane with straight line segments.
The geometry formulas for a triangle are given as;
Area of a triangle=1/2×base×height
Perimeter of Triangle = Sum of All Sides
Circle Geometry Formulas
A circle is a two-dimensional, perfectly round shape. It is formally defined as a set of all points in a plane that are at a fixed, equal distance from a central point. Unlike many other geometric figures, a circle has no corners, vertices, or straight edges.
Formulas for circles in geometry are given as;
Area of Circle = A = π × r^2
Circumference of Circle = C = 2 × π × r
Where, ‘r’ is the radius of a circle.
The value of pi is 3.14
Geometry Formula for a Trapezoid
A trapezoid is a two-dimensional, four-sided shape characterized by having at least one pair of parallel sides. It is commonly visualized as a triangle with its top sliced off parallel to the base
Area of Trapezoid = A = 1/2 × (base1 + base2) × height
Solid (3D) Geometric Formulas
In geometry, a solid is a three-dimensional figure that occupies space and is bounded by a closed surface. Unlike 2D shapes, which only have length and width, solids possess three dimensions, i.e., length, width, depth, and height.
In this section, you will learn all geometry formulas for 3D geometric shapes.
Geometry Formulas for Cylinder
A cylinder is a three-dimensional solid shape characterized by two identical, parallel bases connected by a curved surface.
urved surface area of Cylinder = CSA = 2 × π × r × h
Total surface area of Cylinder = TSA = 2 × π × r × (r + h)
Volume of Cylinder = V = π × r^2 × h
Cone Geometry Formulas
Cone geometry formulas are used to calculate the parameters of a cone. A cone is a three-dimensional geometric shape that narrows down smoothly from a flat base (usually circular) to a single point called the apex or vertex.
The geometry formulas for a cone are given as;
Curved surface area of Cone = CSA = π × r × l
Slant height of Cone = l = √(h^2 + r^2)
Total surface area of Cone = TSA = π × r × (r + l) = π × r × [r + √(h^2 + r^2)]
Volume of Cone = V = 1/3 × π × r^2 × h
Sphere Geometry Formula
A sphere is a perfectly round geometrical object in three-dimensional space. It is defined as the set of all points that are a fixed distance from a central point.
Surface Area of a Sphere = S = 4πr2
Volume of Sphere = V = 4/3 × π × r^3
Geometry Formula Sheet
A geometry formula sheet is a concise reference guide that summarizes mathematical formulas used to calculate the dimensions, area, and volume of geometric figures.
This sheet can help you solve geometric problems if you are preparing for the SAT, GRE, or GMAT.
Geometry Formulas PDF
We will provide you with the list of all geometry formulas in PDF format so you can download it and get help at the time of need.
Conclusion
Geometry formulas are mathematical equations used to calculate various properties of shapes, such as their perimeter, area, volume, and surface area. These formulas are divided into two main categories, including 2D (Plane Geometry) for flat shapes and 3D (Solid Geometry) for three-dimensional objects.
