**Area and Perimeter :**

In this section, we will learn how to find area and perimeter of different shapes.

**Perimeter : **

Perimeter is the distance around a two-dimensional shape such as square or rectangle or triangle.

**Area : **

The amount of space inside the boundary of a two- dimensional shape such as a triangle or circle.

**Square :**

**A square is a four-sided polygon where the lengths of all the four sides will be equal and each vertex angle will be right angle or 90**°** **^{ }**as shown below. **

When the side length is given :

**Area of a Square = a ^{2}**

When the length of the diagonal is given :

**Area of a Square = 1/2 ****⋅ d ^{2}**

**Perimeter of a Square = 4a**

**Rectangle :**

A rectangle is a four-sided polygon where the lengths of opposite sides will be equal and each vertex angle will be 90° or right angle as shown below.

**Area of a Rectangle = l ****⋅ w**

**Perimeter of a Rectangle = 2(l + w)**

**Equilateral Triangle :**

An equilateral triangle is a three-sided polygon where the lengths of all the three sides will be equal and each vertex angle will be 60° as shown below.

**Area of an Equilateral Triangle = √3/4 ⋅ a ^{2}**

**Perimeter of an Equilateral Triangle = 3a**

**Scalene Triangle :**

An scalene triangle is a three-sided polygon where the all the three sides will have unequal lengths and the measures of all the three angles will be different as shown below.

**Area of a Scalene Triangle = √[s(s-a)(s-b)(s-c)**

where s = (a + b + c) / 2

**Perimeter of a Scalene Triangle = a + b + c**

**Quadrilateral :**

A quadrilateral is a four-sided polygon as shown below.

**Area of a Quadrilateral = 1/2 ⋅ d ****⋅ (h _{1} + h_{2})**

**Perimeter of a Quadrilateral = a + b + c + d**

**Parallelogram**** :**

A parallelogram is a four-sided polygon where the opposite sides will be equal and parallel as shown below.

**Area of a Parallelogram = b ⋅ h**

**Perimeter of a Parallelogram = 2(a + b)**

**Rhombus**** :**

A rhombus is a four-sided polygon where the lengths of all the four sides will be equal and opposite sides will be parallel as shown below.

**Area of a Rhombus = 1/2 ****⋅ d _{1}**

**Perimeter of a Rhombus = 4a**

**Trapezoid :**

A trapezoid is a four-sided polygon which has a pair of opposite sides parallel as shown below.

**Area of a Trapezoid = 1/2 ****⋅ h**** ⋅ (a + b)**

**Perimeter of a Trapezoid = a + b + c + d**

**Circle :**

A circle is a round plane figure whose boundary (the circumference) consists of points equidistant from a fixed point (the center). The distance between the center and any point on the circumference is called radius (r).

**Area of a Circle = ****∏****r ^{2}**

**Perimeter of a Circle = 2****∏****r**

**Semicircle :**

A semicircle is a half of a circle or of its circumference as shown below.

**Area of a Semicircle = ****∏****r ^{2 }/ 2**

**Perimeter of a Semicircle = ****∏****r + 2r**

**Quadrant :**

A quadrant is a one-fourth of a circle.

**Area of a Quadrant = ****∏****r ^{2 }/ 4**

**Perimeter of a Quadrant = ****∏****r/2 + 2r**

**Sector of a Circle :**

A sector of a circle is a part of the interior of the circle enclosed by an arc and two radii.

**Area of a Sector = θ/360**°** ⋅ ∏r ^{2}**

**Length of the Arc AB = θ/36****0**°** ⋅ 2∏r**

**Perimeter a Sector = (****θ/36****0**°** ⋅ 2∏r) + 2r**

**Regular Polygon : **

A regular polygon is a polygon that is equiangular (all interior angles are equal in measure) and equilateral (all sides have the same length).

**Area = 1/2**** ⋅ (Apothem x Perimeter) **

**Area = No. of sides**** ⋅ Length of each side**

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After having gone through the stuff given above, we hope that the students would have understood, how to find area and area and perimeter of a 2-D shape.

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