# AREA AND PERIMETER

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.

## Area and Perimeter - Formulas

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  =  a2

When the length of the diagonal is given :

Area of a Square  =  1/2 ⋅ d2

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 ⋅ a2

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

A quadrilateral is a four-sided polygon as shown below. Area of a Quadrilateral  =  1/2 ⋅ d ⋅ (h1 + h2)

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 ⋅ d1 ⋅ d2

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  =  r2

Perimeter of a Circle  =  2r

Semicircle :

A semicircle is a half of a circle or of its circumference as shown below. Area of a Semicircle  =  r2 / 2

Perimeter of a Semicircle  =  r + 2r

A quadrant is a one-fourth of a circle. Area of a Quadrant  =  r2 / 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° ⋅ r2

Length of the Arc AB  =  θ/360° ⋅ 2r

Perimeter a Sector  =  (θ/360° ⋅ 2r) + 2r

Regular Polygon :

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 If you would like to have problems on area and perimeter,

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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