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
If you would like to have problems on area and perimeter,
Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.
Kindly mail your feedback to v4formath@gmail.com
We always appreciate your feedback.
WORD PROBLEMS
Word problems on simple equations
Word problems on linear equations
Word problems on quadratic equations
Area and perimeter word problems
Word problems on direct variation and inverse variation
Word problems on comparing rates
Converting customary units word problems
Converting metric units word problems
Word problems on simple interest
Word problems on compound interest
Word problems on types of angles
Complementary and supplementary angles word problems
Markup and markdown word problems
Word problems on mixed fractions
One step equation word problems
Linear inequalities word problems
Ratio and proportion word problems
Word problems on sets and Venn diagrams
Pythagorean theorem word problems
Percent of a number word problems
Word problems on constant speed
Word problems on average speed
Word problems on sum of the angles of a triangle is 180 degree
OTHER TOPICS
Time, speed and distance shortcuts
Ratio and proportion shortcuts
Domain and range of rational functions
Domain and range of rational functions with holes
Graphing rational functions with holes
Converting repeating decimals in to fractions
Decimal representation of rational numbers
Finding square root using long division
L.C.M method to solve time and work problems
Translating the word problems in to algebraic expressions
Remainder when 2 power 256 is divided by 17
Remainder when 17 power 23 is divided by 16
Sum of all three digit numbers divisible by 6
Sum of all three digit numbers divisible by 7
Sum of all three digit numbers divisible by 8
Sum of all three digit numbers formed using 1, 3, 4
Sum of all three four digit numbers formed with non zero digits
Sum of all three four digit numbers formed using 0, 1, 2, 3
Sum of all three four digit numbers formed using 1, 2, 5, 6
©All rights reserved. onlinemath4all.com
Recent Articles
-
Linear vs Exponential Growth
May 23, 22 01:59 AM
Linear vs Exponential Growth - Concept - Examples
-
Exponential vs Linear Growth Worksheet
May 23, 22 01:42 AM
Exponential vs Linear Growth Worksheet
-
SAT Math Questions on Exponential vs Linear Growth
May 23, 22 01:34 AM
SAT Math Questions on Exponential vs Linear Growth