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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.
 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.
 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)
 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.
 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)
 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) = $1/2 × b h$ Hero's formula - A greek mathematician, Hero, gave the formula of area of triangle as follows: Let $a$, $b$ and $c$ be the sides of a △ ABC Then, s = $\frac12 (a+b+c)$ Area of △ ABC = $\sqrt{s(s-a)(s-b)(s-c)}$ 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.
 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 = $l(AB) + l(BC) + l(CD) + l(DE) + l(AE)$