# Area, Perimeter, and Volume Formulas of Basics Geometric Shapes

## What is Area?

The word “area” refers to a free space. A shape’s length and width are used to compute its area. Both length and width are unidimensional but area on the other hand is two-dimensional and is typically expressed as square units.

Area of a shape = length x width

## What is Perimeter?

A perimeter is a two-dimensional figure and originated from a Greek word, “peri” which means surrounding, and “metron,” which means measure.

By summing up the lengths of each shape’s sides and edges, one can determine a shape’s perimeter in geometry. Thus, a shape’s perimeter is the total distance around it.

The perimeter of a shape = Sum of all sides

## Difference Between Area and Perimeter?

 Area Perimeter In a two-dimensional plane, the area is the space occupied by a closed shape. A closed shape’s overall length around the exterior is its perimeter. It is the shape’s inside space. It is the outer length around the shape. Square units are used to measure area. Perimeter is quantified in linear units. For example: the area required to set up a toddler’s bed. For example: creating a fencing for the toddler’s bed.

## Area and Perimeter Formulas of 2D Geometric Shapes

### 1. Area and Perimeter Formulas for a Square

Area of a Square = side(s) x side(s)

= 24 x 24

= 576 m²

Perimeter of a Square = side(s) + side(s) + side(s) + side(s)

= 4 side(s)

= 4 x 24

= 96 m

### 2. Area and Perimeter Formulas for a Rectangle

Area of a Rectangle = length(l) x breadth(b)

= 6 x 3

= 18 cm²

Perimeter of a Rectangle = 2(length(l) + breadth(b))

= 2 (6 + 3)

= 2 (9)

= 18cm

### 3. Area and Perimeter Formulas for a Triangle

Area of a Triangle = 1/2 × b × h

= 1/2 x 4 x 3

= 6 cm²

Perimeter of a Triangle = side(s)1 + side(s)2 + side(s)3

= 3 + 4 + 5

= 12 cm

### 4. Area and Perimeter Formulas for a Circle

Area of a Circle = πr²

= 22/7 x 7 x 7

= 154 m²

The perimeter of a Circle = 2πr

= 2 x 22/7 x 7

= 44 m

### 5. Area and Perimeter Formulas for a Parallelogram

Area of Parallelogram= base x height

= 10 x 3.5

= 35 cm²

Perimeter of Parallelogram = 2 x (base + height)

= 2 x (10 + 3.5)

= 2 x 13.5

= 27 cm

### 6. Area and Perimeter Formulas for a Rhombus

Area of Rhombus = (d1 x d2)/2

= 1/2 × d₁ × d₂

= 1/2 × 16 × 30

= 240 cm²

Perimeter of Rhombus = 4 x side

= 4 x 17

= 68 cm

### 7. Area and Perimeter Formulas for a Trapezoid

Area of Trapezoid = (base1 + base2) x height / 2

= (2 + 4.5) x 2/2

= 6.5 x 1

= 6.5 square units

The perimeter of the Trapezoid = sum of all sides

= (3 + 2 + 2 + 4.5)

= 11.5 units

### 8. Area and Perimeter Formulas for a Hexagon

Area of Hexagon = (3 x √3 x side^2)/2

= 3√3 7×7 / 2

= 3√3 49 / 2

= 147 √3 / 2

= 127.30 cm²

The perimeter of the Hexagon = 6 x side

= 6 x 7

= 42 cm

### 9. Area and Perimeter Formulas for a Octagon

Area of Octagon = (2 x (1 + √2) x side^2)

= (2 +2√2) x 5 x 5

= 4.82 x 25

= 120.7 m²

Perimeter of Octagon = 8 x side

= 8 x 5

= 40 m

### 10. Area and Perimeter Formulas for a Ellipse

Area of Ellipse = π x a x b

= 22/7 x 10 x 5

= 157.1 cm²

Perimeter of Ellipse (circumference) = 2π( √(a^2 + b^2)/2)

= 2 x 22/7 (7.91)

= 49.67 cm

## Area and Volume Formulas of 3D Geometric Shapes

### 1. Area and Volume Formulas for a Prism

Surface Area of Prism = ab + 3bh

= (7 cm  × 10 cm) + (3  × 10 cm × 18 cm)

= 70 cm² + 540 cm²

= 610 cm²

Volume of Prism = base area x height

= (1/2 x 10 x 18) x 18

= 90 x 18

= 1620 cm³

### 2. Area and Volume Formulas for a Torus

Area of Torus = 4π^2 x R x r

= 4 x 22/7 x 22/7 x 7 x 3

= 84 x 22/7 x 22/7

= 829.7 mm²

Volume of Torus = (2π^2 x R x r^2)

= 2 x 22/7 x 22/7 x 7 x 3 x 3

= 1244.5 mm³

### 3. Area and Volume Formulas for a Pyramid

Area of Pyramid = Base area +1/2(perimeter × slant height)

=  10 x 10 + 1/2 x 4 x 10 x 17.3

=  100 + 2 x 10 x 17.3

=  100 + 346

=  446 cm²

Volume of Pyramid = (1/3) x area of base x height

= 1/3 x 10 x 10 x 18

= 600 cm³

### 4. Area and Volume Formulas for a Cylinder

Area of Cylinder = (2 x π x radius x height) + (2 x π x radius^2)

= 2πr (r + h)

= 2 x 22/7 x 3 (3 + 5)

= 2 x 66/7 (8)

= 150 cm²

Volume of Cylinder = π x r² x height

=  π x 3 x 3 x 5

= π ( 9 ) 5

= (3. 14) (45)

= 141.30 cm³

### 5. Area and Volume Formulas for a Sphere

Area of Sphere = 4 x π x radius^2

= 4 x 22/7 x 9 x 9

= 1018 cm²

Volume of Sphere = (4/3) x π x radius^3

= 4/3 x 22/7 x 9 x 9 x 9

= 3054.8 cm³

### 6. Area and Volume Formulas for a Cone

Total Surface Area of Cone = π x radius x (radius + slant height)

= 22/7 x 8 x (8 + 14.42)

= 563.7 cm²

Volume of Cone  = (1/3) x π x radius^2 x height

= 1/3 x 22/7 x 8 x 8 x 12

= 804.5 cm³

### 7. Area and Volume Formulas for a Cube

Total surface area of a cube = 6 × side²

= 6 x 10 x 10

= 600 m²

Volume of Cube  = side³

= 10 x 10 x 10

= 1000 m³

## Conclusion: Mastering the Basics of Area, Perimeter, and Volume for Different Shapes is Essential for Maths

Area, Perimeter, and Volume are three significant and essential mathematical concepts. In addition to aiding in the quantification of physical space, they serve as a basis for more difficult mathematical concepts found in algebra, trigonometry, and calculus.

Knowing how much space you have and learning how to accurately put forms together will be helpful for tasks that people use on a regular basis, such as painting a room, buying a house, remodeling a kitchen, or adding a deck.