Mathematical Formulas For Shapes Pdf

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 × \((base_1 + base_2)\) × height

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

Area of a Circle = A = π×r ²
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 = πr ² h
The curved surface area of a cone = πrl
Total surface area of a cone = πr(r+l) = πr[r+√(h ² +r ² )]
Volume of a Cone = V = ⅓×πr ² h
Surface Area of a Sphere = S = 4πr ²
Volume of a Sphere = V = 4/3×πr ³

where,

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

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

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 the 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 and 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 and 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^⅓ 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, A = 2πrh + 2πr² Curved Surface Area, 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, A = πr(r+l) = πr[r+√(h²+r²)] Curved Surface Area, A_c = πrl Volume, V = ⅓πr²h 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 = ⁴⁄₃πr³ Diameter = 2r Where, 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?

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.

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

Solution:
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?

The geometry formulas of a cuboid are listed below:

Surface Area of cuboid, A = 2(lb + bh + hl)
Volume of cuboid, V = lbh
Space diagonal of cuboid, d = √(l² + b² +h²)

Where,

l= length
b= breadth
h= height

What Are the Geometry Formulas of a Rectangle?

The geometry formulas of a rectangle are listed below:

Perimeter of a rectangle = 2(l + w)
Area of rectangle = lw
Diagonal of a rectangle, d = √(l² + w²)

Where,

l = length of a rectangle
w = width of a rectangle

What Are the Geometry Formulas of a Cone?

The geometry formulas of a cone are listed below:

Total surface area of cone, A = πr(r+l) = πr[r+√(h²+r²)]
Curved surface area of cone, A_c = πrl
Volume of cone, V = ⅓πr²h
Slant Height of cone, l = √(h²+r²)
Base Area, A_b = πr²

Where,

r= radius of a cone
h= height of a cone
l = slant height

What Are the Geometry Formulas of a Circle?

The geometry formulas of a circle are listed below:

Circumference = 2πr
Area = πr²
Diameter = 2r

Where, r = radius of a circle