AREA AND PERIMETER

Area : 

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

Perimeter : 

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

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

Quadrilateral :

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  =  2∏r

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

Quadrant :

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° ⋅ 2∏r

Perimeter a Sector  =  (θ/360° ⋅ 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) 

Perimeter  =  No. of sides ⋅ Length of each side

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