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Area and Perimeter of regular polygons


Rectangle

A rectangle is a quadrilateral with four right angles. The opposite sides of a rectangle are equal.
Graphical representation of rectangle

Area of a rectangle = $length × breadth$

Area of a rectangle ABCD = $l × b$

Perimeter of a rectangle = $2 (length + breadth)$

Perimeter of a rectangle ABCD = $2 (l + b)$




Square

A square is a special case of a rectangle. A rectangle whose all the sides are equal is a square.
Graphical representation of square

Area of a square = $side^2$

Area of a square ABCD = $a^2$

Perimeter of a square = $4 × side$

Perimeter of a square ABCD = $4 × a$




Circle

A circle is a plane figure whose boundary (circumference) consists of points equidistant from a fixed point (called its centre)
Graphical representation of circle

Area of a circle = $π × radius^2$

Area of a circle with centre O and radius OA (r) = $π × r^2$

Perimeter (Circumference) of a rectangle = $2 × π × radius$

Perimeter (Circumference) of a circle with centre O and radius OA (r) = $2 × π × r$




Sector

A sector of a circle is an area enclosed by two radii and an arc of a circle.
Graphical representation of a Sector

Area of a circle = $π × radius^2 × C/360$

Area of a circle with centre O and radius OA (r) = $π × r^2 × C/360$
(when C is in degrees)

Perimeter of a sector = $(2 × radius) + $ (Length of arc AB)

Perimeter of a sector with radius r and arc AB = $(2 × r) + 2 π r × Angle (AOB)/360$
= $2r + 2π r × C/ 180$
(when C is in degrees)




Triangle

A circle is a plane figure whose boundary (circumference) consists of points equidistant from a fixed point (called its centre)
Graphical representation of triangle

Area of a triangle = $ 1/2 × height × base$

Area of a triangle ABC with height (AD) and base (BC) = $ 1/2 × AD × BC$
Area of a triangle ABC with height (h) and base (b) = $ 1/2 × b h $

Perimeter of a triangle = sum of the lengths of all the three sides

Perimeter of a triangle ABC = $l(AB) + l(BC) + l(AC)$




Pentagon

A regular pentagon is a polygon with five equal sides. This also makes all the five angles in pentagon equal.
A pentagon can be considered as 5 equal triangles put together. Hence area of a pentagon is 5 times the area triangle.
Graphical representation of pentagon

Area of a pentagon = $ 5 × (1/2 × height × base)$

Area of a pentagon ABCDE = $ 5 × (1/2 × b × h)$

Perimeter of a pentagon = sum of the lengths of all the five sides

Perimeter of a pentagon ABCDE = $l(AB) + l(BC) + l(CD) + l(DE) + l(AE)$