In mathematics, we learn about various shapes. These shapes may be two-dimensional(2d shapes) or three-dimensional(3d shapes). In this article, we will discuss what is a two-dimensional shape & the area and perimeter of two-dimensional shapes.

## What is a Two-dimensional shape?

Two-dimensional shapes are those shapes that have length, breadth, height, or radius but not any thickness.

Examples of two-dimensional(2d) shapes are square, rectangle, circle, triangle, parallelogram, kite, polygon, etc.

### Perimeter & area of two-dimensional shapes

The perimeter of 2d shapes is the length of their boundary and the area of 2d shapes is the surface that is covered by their perimeter.

For example, the perimeter of a square is 4×side because we get the length of their boundary by the sum of all four sides.

### Area and Perimeter of 2d shapes formulas

We are discussing area and perimeter formulas for all shapes that are 2d:

The perimeter of the square = 4×side

Area of square = side×side

Perimeter of rectangle = 2×(Length+Breadth)

Area of rectangle = Length×Breadth

The perimeter of the triangle = Sum of all sides

The perimeter of the Equilateral triangle = 3×side

Area of Right-angled triangle = (1/2)×Base×Height

Area of triangle by Heron's Formula = √{s(s-a)(s-b)(s-c)} where s=semiperimeter and a,b,c are sides of triangle

The formula for the circumference of a circle = 2Ï€r

Area of circle = Ï€r² where, r = radius of the circle and Ï€ = 22/7 or 3.14

The perimeter of the rhombus = 4×side

Area of rhombus = (1/2)×D₁×D₂ where D₁ & D₂ are diagonals of a rhombus.

The perimeter of the parallelogram = Sum of all sides

Area of parallelogram = Base × Height

### Find the perimeter and area of the polygon:

To find the perimeter and area of the polygon we are taking area and perimeter word problems for better understanding:

**1. If the length of each side of a triangle is 4cm. Find the perimeter of a triangle.**

The perimeter of an equilateral triangle=3×side

= 3×4cm

= 12cm

**2. Find the area and perimeter of a rectangle if its length is 13 cm and width is 10cm long.**

Perimeter of rectangle=2×(Length+Breadth)

= 2×(13cm+10cm)

= 2×23cm

= 46cm

Area of Rectangle=Length×Breadth

=13cm×10cm

=130 sq. cm.

**3. Find the perimeter and area of the polygon if the length of all four sides is 3cm each.**

Perimeter of square=4×side

=4×3cm

=12cm

Area of square=side×side

=3cm×3cm

=9 sq. cm.

**4. If the length of the sides of a quadrilateral is 3cm, 5cm, 4cm, and 3cm long then find the perimeter of a quadrilateral.**

The perimeter of Quadrilateral=Sum of all sides

=3cm+5cm+4cm+3cm

=15cm

**5. Find the perimeter of the square if its side is 10cm long.**

Perimeter of Square=4×side

=4×10cm

=40cm

**6. Find the area of a rectangle if its length and breadth are 12cm and 10cm long respectively.**

Area of Rectangle formula=Length×Breadth

=12cm×10cm

=120 sq. cm.

**7. Find the perimeter of a parallelogram if the length of their adjacent sides is 7cm and 5cm.**

The formula for the perimeter of Parallelogram=Sum of all sides

=7cm+5cm+7cm+5cm

=24cm

**8. Find the perimeter of a rectangle for a length is 15cm and a breadth is 11cm long.**

Perimeter of Rectangle=2×(Length+Breadth)

=2×(15cm+11cm)

=2×26cm

=52cm

**9. Find the area and perimeter of the square if the length of each side is 6cm long.**

Area of square=side×side

=6cm×6cm

=36 sq. cm.

Perimeter of square=4×side

=4×6cm

=24cm.