# Area and Perimeter Formulas of All 2 D Shapes

The meaning of 2-D shapes is 2 dimensional shapes. In Geometry, a two dimensional shape is defined as a plane figure having two dimensions- length, and breadth (or width). 2 dimensional shapes are also known as rectilinear figures or plane figures. Students can also download the HD printout of Area and Perimeter Formulas of all 2 D Shapes and can stick on their pinboard. This will help them to revise and learn all the formulas for doing sums on 2-D shapes.

## Area and Perimeter of Plane figures

Before getting into the formulas of area and perimeter of plane figures, let us understand the meaning of Perimeter and Area.

Perimeter: The perimeter of a plane figure is the length of its boundary.

Area: The area of a plane figure is the amount of surface enclosed by its sides.

In simple language, Perimeter is the distance around the outside of a shape and Area is the space inside the shape.

## Area and Perimeter Formulas of All 2 D Shapes

If a, b, and c be the three sides of a triangle , then
•  Perimeter of triangle = (a + b + c) units
• Area of triangle (Heron’s formula) = √[s(s – a) (s – b) (s – c)] where s (semi-perimeter) = 1/2 (a + b + c)   sq. units
•  Area of triangle = 1/2 × base × height   sq. units
•  Area of an equilateral triangle = (√3a2)/4  sq. units
• Area of an isosceles triangle = b/4 (4a2– b2)  sq. units
• Area of a right-angled triangle = 1/2 × base × height  sq. units

## Formulas for Perimeter and Area of Parallelogram

A Parallelgram is a four sided closed figure with opposite sides equal and parallel.

• Perimeter of parallelogram = 2 (sum of adjacent sides) units

• Area of parallelogram = (base × correspoding height)   sq. units

## Formulas for Perimeter and Area of Rhombus

A Rhombus is a four sided closed figure with all sides equal and opposite sides parallel.

• Area of rhombus = (base × corresponding height)  sq. units

• Area of rhombus = (1/2 × length of one diagonal × length of other diagonal)  sq. units

• Perimeter of rhombus = (4 × side)  units

## Formulas for Perimeter and Area of Rectangle

A Rectangle is a four sided closed figure with opposite sides equal and each angle 90°.
If l be the length of the rectangle and b its breadth, then

• Perimeter of rectangle = 2(l + b)  units

• Area of rectangle = (l × b)  sq. units

• Diagonal of rectangle = √(l² + b²)  units

## Formulas for Perimeter and Area of Square

A Square is a four sided closed figure with all sides equal and each angle 90°.
If a be the length of an edge of a square then,

• Perimeter of square = 4 a  units

• Area of square = a × a =  a sq. units

• Diagonal of square = (√2)a  units

## Perimeter and Area of the Trapezium

A Trapezium is a four sided closed figure with any one pair of sides parallel to each other.

•  Area of trapezium = 1/2 (sum of parallel sides) × (perpendicular distance between them)

= 1/2 (a + b) × h   sq. units

(if  a and b are the parallel sides of the trapezium and h be the perpendicular distance between them)

• Perimeter = sum of 4 sides

## Circumference and Area of Circle

The path traced by a moving point, which always remains at a fixed distance from a fixed point, is called a Circle.

If r be the radius and d be the diameter of the circle, then

• Diameter (d) = 2r  units
• Circumference of circle = 2πr = πd (where π = 3.14 or 22/7) units
• Area of circle = πr² sq. units
• Area of ring = Area of outer circle – Area of inner circle

= π (R² – r²)  sq. units

• 1 revolution by a circular wheel = circumference of that circular wheel

## Circumference and Area of Semi-circle

Every diameter divides a circle into two equal parts, each of which is called a Semi-circle.

If r be the radius, then

• Circumference of semi-circle = πr + 2r  (where π = 3.14 or 22/7)  units
• Area of semi-circle = 1/2 πr²   sq. units

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