Area and Perimeter :
In this section, we will learn how to find area and perimeter of different shapes.
Perimeter is the distance around a two-dimensional shape such as square or rectangle or triangle.
The amount of space inside the boundary of a two- dimensional shape such as a triangle or circle.
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
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
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)
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
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
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
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° ⋅ 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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