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

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)

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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