Geometry Formulas

About Geometry Formulas

Geometry formulae are used to calculate geometric shape dimensions, perimeter, area, surface area, volume, and so on. Geometry is a branch of mathematics that studies the links between points, lines, angles, surfaces, measurements, and properties of solids. Geometry is divided into two types: 2D or plane geometry and 3D or solid geometry. 2D shapes, such as squares, circles, and triangles, are flat shapes with only two dimensions: length and width. 3D objects, such as a cube, cuboid, sphere, cylinder, or cone, have three dimensions: length, width, and height or depth.

Geometry formulae are used to calculate the dimensions, perimeter, area, surface area, volume, and other properties of 2D and 3D geometric shapes. 2D shapes include flat shapes such as squares, circles, and triangles, while 3D shapes include cube, cuboid, sphere, cylinder, cone, and others. The following are the basic geometry formulas:

Square	Triangle	Circle
Rectangle	Eclipse	Trapezoid

List of Geometry Formulas

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
Area of a Circle = A = π×r²
Circumference of a Circle = 2πr
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 = ?×πr²h
Surface Area of a Sphere = S = 4πr²
Volume of a Sphere = V = 4/3×πr³

Where,

r = Radius
h = Height, and
l = Slant height

SHAPES	FORMULAS
1. Right Triangle	Pythagoras Theorem: a² + b² = c² Area = ½ ab Perimeter = a + b + √(a² + b²) Where, c = hypotenuse of a triangle a = altitude of a triangle b = base of a triangle
2. Triangle	Perimeter, P = a + b + c Area, A = ½ bh Height, h = 2(A/b) Where, a,b,c are three sides of a triangle.
3. Rectangle	Perimeter = 2(l + w) Area = lw Diagonal, d = √(l² + w²) Where, l = length of a rectangle w = width of a rectangle
4. Parallelogram	Perimeter, P = 2(a + b) Area, A = bh Height, h = A/b Base, b = A/h Where, a & b are the sides of a parallelogram h = height of a parallelogram
5.Trapezium	Area, A = ½(a + b)h Height, h = 2A/(a + b) Base, b = 2(A/h) – a Where, a & b are the parallel sides h = distance between two parallel sides
6. Circle	Circumference = 2πr Area = πr² Diameter = 2r Where, r = radius of a circle
7. Square	Perimeter, P = 4a Area, A = a² Diagonal, d = a√2 Side, a = √A = d/2√2 Where, a = side of a square
8. Arc	Arc Length, L = rθ Area, A = ½r²θ Here, θ is the central angle is radians. Where, r = radius
9. Cube	Area, A = 6a² Volume, V = a³ Edge, a = V^? Space diagonal = a√3 Where, a = side of a cube
10. Cuboid	Surface Area, A = 2(lb + bh + hl) Volume, V = lbh Space diagonal, d = √( l² + b² +h²) Where, l = length b = breath h = height
11. Cylinder	Total Surface Area(TSA), A = 2πrh + 2πr² Curved Surface Area (CSA), A_c = 2πrh Volume, V = πr²h Base Area, A_b = πr² Radius, r = √(V/πh) Where, r = radius of a cylinder h = height of a cylinder
12. Cone	Total Surface Area(TSA), A = πr(r+l) = πr[r+√(h²+r²)] Curved Surface Area (CSA), A_c = πrl Volume, V = ?πr²h Slant Height, l = √(h²+r²) Base Area, A_b = πr² Where, r = radius of a cone h = height of a cone l = slant height
13. Sphere	Surface Area, A = 4πr² Volume, V = ?⁄?πr³ Diameter = 2r Where, r = radius of a sphere