# FORMULAS FOR SHAPES

Circle :

Formulas :

Area of circle  =  Πr2

Circumference of circle  =  2Πr

Example problems of area of circle

Example problems of circumference of circle

Semicircle :

Formulas :

Area of semicircle  =  Πr2 / 2

Circumference of circle  =  Πr

Example problems on semi circle

Formulas :

Area of quadrant  =  Πr/ 4

Equilateral Triangle :

Formulas :

Area of equilateral triangle  =  (√3/4)a2

Perimeter of equilateral triangle  =  3a

Example problems on equilateral triangle

Scalene Triangle :

Formulas :

Area of scalene triangle  =  √[s(s-a)(s-b)(s-c)]

Perimeter of scalene triangle  =  a + b +  c

Example problems on scalene triangle

Parallelogram :

Formulas :

Area of parallelogram  =  b x h

Perimeter of parallelogram =  2(a + b)

Example problems of perimeter of parallelogram

Formulas :

Area of quadrilateral  =  (1/2) x d x (h+ h2)

Perimeter of quadrilateral  =  a + b + c + d

Example problems of area of quadrilateral

Rectangle :

Formulas :

Area of rectangle  =  l x w

Perimeter of rectangle  =  2(l + w)

Examples problems on area of rectangle

Examples of perimeter of rectangle

Square :

Formulas :

Area of square  =  a x a

Perimeter of square  =  4a

Examples problems on area of square

Examples problems on perimeter of square

Rhombus :

Formulas :

Area of rhombus  =  (d1 x d2) / 2

Perimeter of rhombus  =  4a

Examples problems on perimeter of rhombus

Trapezoid :

Formulas :

Area of trapezoid  =  h(a + b) / 2

Perimeter of trapezoid  =  a + b + c + d

Examples problems on area of trapezoid

Sector :

Formulas :

Length of arc (l)  = (θ/360)  2Πr

When we know the radius "r" of the circle and central angle "θ" of the sector :

Area of the sector  =  (θ/360°⋅ Π r2

When we know the radius "r" of the circle and arc length "l"

Area of the sector = (l ⋅ r) / 2

Worksheet for length of arc

Area of sector worksheet

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WORD PROBLEMS

Word problems on simple equations

Word problems on linear equations

Algebra word problems

Word problems on trains

Area and perimeter word problems

Word problems on direct variation and inverse variation

Word problems on unit price

Word problems on unit rate

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

Double facts word problems

Trigonometry word problems

Percentage word problems

Profit and loss word problems

Markup and markdown word problems

Decimal word problems

Word problems on fractions

Word problems on mixed fractrions

One step equation word problems

Linear inequalities word problems

Ratio and proportion word problems

Time and work word problems

Word problems on sets and venn diagrams

Word problems on ages

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

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Profit and loss shortcuts

Percentage shortcuts

Times table shortcuts

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

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