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.
Mensuration Calculators
18. Heron's Triangle Area Calculator
20. Regular Polygon Area Calculator
22. Circle Sector Area Calculator
Please click the below link to get calculators in other areas of math.
Please click the below link to get printable math worksheets
Founder of Mensuration:
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Archimedes is remembered as the greatest mathematician of ancient area.He is one of the most famous Greek mathematicians contributed significantly in geometry regarding the area of plane figures and areas as well as volumes of curved surfaces. |
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.
Apart from our aim towards the exam, like preparing for exams,aiming to score more marks in exams, we need the formulas and concepts of this topic to solve some problems in our day to day life also.
A painter charges $5 per square meter to paint a wall.Mr.Joseph has wall whose length is 5m and width is 4m.How much does Mr.Joseph have to pay to paint the wall?
This is a problem we usually face in our day to day life.
To find a solution to this problem, we need to determine the area of the wall.After determining the area of the wall, we can easily find the total money required to paint the wall.To find the area of the wall, we need a formula.That we get from this topic.
Let us look at another example.
We have cylindrical tank whose radius and height is 1 meter and 3 meters respectively.Find the volume of water required to fill up the tank.
To solve the above problem we need the formula to find the volume of the cylinder. To solve these type of problems in our life, we require the concepts of volume.For different shapes we have different formulas.
You can click the following links to know about the given sub topics of mensuration
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Area of rectangle = L x W
Here "L" represents length of the rectangle and "W" represents width of the rectangle | |
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Perimeter of rectangle = 2 (L + W)
Here "L" represents length of the rectangle and "W" represents width of the rectangle |
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Area of square = a x a
Here "a" represents side length of the square. | |
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Perimeter of square = 4 a
Here "a" represents side length of the square. |
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Area of parallelogram = b x h
Here "b" represents base length and "h" represents height. | |
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Area of parallelogram = 2 (L + W)
Here "L" represents length and "W" represents width of the parallelogram. |
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Area of Rhombus = (1/2) x (d₁ x d₂)
Here "d1" and "d2" are representing length of both diagonals of the rhombus. | |
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Perimeter of Rhombus = 2 √d₁² + d₂² (or) 4 a
By using either of these formulas we can find the perimeter of the rhombus. Here "d1" and "d2" are representing length of both diagonals of the rhombus and "a" represents side length of the rhombus. |
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area of quadrilateral = (1/2) x d x (h₁ + h₂)
Here "d" represents length of diagonal. "h1" and "h2" are representing perpendicular length of the quadrilateral. |
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area of quadrilateral = (1/2) x d x (h₁ + h₂)
Here "d" represents length of diagonal. "h1" and "h2" are representing perpendicular length of the quadrilateral. |
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area of triangle = (1/2) x b x h
Here "b" represents the base length and "h" represents height of the triangle. |
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area of scalene triangle = √s(s-a)(s-b)(s-c)
Here "s" represents the sum of the sides of the triangle/2. The side length of the triangle mentioned as a,b and c. | |
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Perimeter of scalene triangle s = (a + b + c)/2
Here the side length of the triangle mentioned as a,b and c. |
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area equilateral triangle = (√3/4) a²
Here "a" represents the side length of the triangle. | |
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perimeter of area equilateral triangle P = a + b + c
Here "a","c" and "c" are representing the side length of the triangle. |
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area of sector = (θ/360) x Π r ² square units
= (1/2) x l r square units Here "θ", "r" and "l" are representing angle formed by two radii, radius of the sector and length of arc respectively. | |
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Perimeter of sector = L + 2 r
Here "L" represents length of arc and "r" represents radius of the sector. |
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Area of circle = Π r²
Here "r" represents radius of the circle. | |
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Circumference of circle = 2 Π r
Here "r" represents radius of the circle. |
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Area of Semicircle = (1/2) Π r²
Here "r" represents radius of the semicircle. | |
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Perimeter of semicircle = Πr
Here "r" represents radius of the semicircle. |
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Area of quad-rant = (1/4) Π r²
Here "r" represents radius of the quadrant. |
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curved surface area of cylinder = 2 Π r h<
Here "r" and "h" are representing radius and height of the cylinder. | |
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total surface area of cylinder = 2 Π r (h + r)
Here "r" and "h" are representing radius and height of the cylinder. | |
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Volume of cylinder = Π r2h
Here "r" and "h" are representing radius and height of the cylinder. |
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Curved surface area of cone = Π r L
Here "r" and "L" are representing radius and slant height of the cone. | |
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Total surface area of cone = Π r (L + r)
Here "r" and "L" are representing radius and slant height of the cone. | |
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Volume of cone = (1/3)Π r2 h
Here "r" and "h" are representing radius and height of the cone. |
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Curved surface area of sphere = 4Π r2
Here "r" represents radius of the sphere. | |
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Volume of sphere = (4/3)Π r3
Here "r" represents radius of the sphere. |
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