MENSURATION
Mensuration is one of the branches of mathematics.This means measurement.It is is being done in our life in many situations.
For example,
A Length of cloth we need for stitching,the area of a wall which is being painted, perimeter of the circular garden to be fenced, quantity of water needed to fill the tank. For these kind of activities, we are doing measurements for further needs.
Here, we are going to cover three areas here.
1.Perimeter
2.Area
3.Volume
Apart from the examples and practice questions in the above three areas, we also give calculators in this topic which can be used by the students to check their answers which they have found for the questions they have.You can use any of the given calculators to get answer for your questions in seconds.
For example, in his development of integration and calculus, he tried to find a value for π by using circumscribed and inscribed polygons, eventually using 96 sided polygons inside and outside a circle to generate a value for Pi of between 31⁄7 (approximately 3.1429) and 310⁄71 (approximately 3.1408). This range of values is extremely accurate, as the actual value is 3.1416. This is just one example of his inventions.
In this topic we are going study about perimeter, area and volume of different shapes like a cylinder, cone, sphere, hemisphere etc..These shapes are called geometric shapes.
Formulas
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
Quadrant :
Formulas :
Area of quadrant = Πr2 / 4
Example problems on quadrant
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
Right Triangle :
Formula :
Area of right triangle = (b x h) / 2
Parallelogram :
Formulas :
Area of parallelogram = b x h
Perimeter of parallelogram = 2(a + b)
Example problems of perimeter of parallelogram
Quadrilateral :
Formulas :
Area of quadrilateral = (1/2) x d x (h1 + 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 area of rhombus
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
Cylinder :
Formulas :
Curved surface area of cylinder = 2Πrh
Total surface area of cylinder = 2Πr(h + r)
Volume of cylinder = Πr2h
Cone :
Formulas :
Curved surface area of cone = Πrl
Total surface area of cone = 2Πr(l + r)
Volume of cone = Πr2h / 3
Sphere :
Formulas :
Surface area of sphere = 4Πr2
Volume of sphere = 4Πr3 / 3
Hemisphere :
Formulas :
Curved surface area of hemisphere = 2Πr2
Total surface area of hemisphere = 3Πr2
Volume of hemisphere = 2Πr3 / 3
Mensuration Calculators
18. Heron's Triangle Area Calculator
20. Regular Polygon Area Calculator
22. Circle Sector Area Calculator
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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
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