# 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 concepts.

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

1. Rectangle Area Calculator

2. Acreage Calculator

3. Circle Calculator

4. Sphere Calculator

5. Hemisphere Calculator

6. Cone Calculator

7. Cylinder Calculator

8. Rectangle Calculator

9. Kite Area Calculator

10. Cube Volume Calculator

11. Cube Area Calculator

12. Pyramid Calculator

13. Square Calculator

14. Barrel Volume Calculator

15. Pipe Volume Calculator

16. Rhombus Area Calculator

17. Cuboid Calculator

18. Heron's Triangle Area Calculator

19. Trapezium 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.

Math Calculators

## Founder of Mensuration:

 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

 Area of rectanglePerimeter of rectangleClick the button below to get the formula instantly jQuery UI Accordion - Default functionality .ui-widget-overlay,.ui-state-disabled,ui-button{background:#fff;border:1px solid #fff;color:#b9cd6d;font-weight:bold} Area of rectangle = L x W Here "L" represents length of the rectangle and "W" represents width of the rectangle jQuery UI Dialog functionality .ui-widget-overlay,.ui-state-disabled,ui-button{background:#fff;border:1px solid #fff;color:#b9cd6d;font-weight:bold} Perimeter of rectangle = 2 (L + W) Here "L" represents length of the rectangle and "W" represents width of the rectangle

 Area of squarePerimeter of squareClick the button below to get the formula instantly jQuery UI Dialog functionality .ui-widget-overlay,.ui-state-disabled,ui-button{background:#fff;border:1px solid #fff;color:#b9cd6d;font-weight:bold} Area of square = a x a Here "a" represents side length of the square. jQuery UI Dialog functionality .ui-widget-overlay,.ui-state-disabled,ui-button{background:#fff;border:1px solid #fff;color:#b9cd6d;font-weight:bold} Perimeter of square = 4 a Here "a" represents side length of the square.

 jQuery UI Dialog functionality .ui-widget-overlay,.ui-state-disabled,ui-button{background:#fff;border:1px solid #fff;color:#b9cd6d;font-weight:bold} Area of parallelogram = b x h Here "b" represents base length and "h" represents height. jQuery UI Dialog functionality .ui-widget-overlay,.ui-state-disabled,ui-button{background:#fff;border:1px solid #fff;color:#b9cd6d;font-weight:bold} Area of parallelogram = 2 (L + W) Here "L" represents length and "W" represents width of the parallelogram.

 jQuery UI Dialog functionality .ui-widget-overlay,.ui-state-disabled,ui-button{background:#fff;border:1px solid #fff;color:#b9cd6d;font-weight:bold} Area of Rhombus = (1/2) x (d₁ x d₂) Here "d1" and "d2" are representing length of both diagonals of the rhombus. jQuery UI Dialog functionality .ui-widget-overlay,.ui-state-disabled,ui-button{background:#fff;border:1px solid #fff;color:#b9cd6d;font-weight:bold} 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.

 jQuery UI Dialog functionality .ui-widget-overlay,.ui-state-disabled,ui-button{background:#fff;border:1px solid #fff;color:#b9cd6d;font-weight:bold} 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.

 Area of trapezium jQuery UI Dialog functionality .ui-widget-overlay,.ui-state-disabled,ui-button{background:#fff;border:1px solid #fff;color:#b9cd6d;font-weight:bold} 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.

 Area of triangle jQuery UI Dialog functionality .ui-widget-overlay,.ui-state-disabled,ui-button{background:#fff;border:1px solid #fff;color:#b9cd6d;font-weight:bold} area of triangle = (1/2) x b x h Here "b" represents the base length and "h" represents height of the triangle.

 jQuery UI Dialog functionality .ui-widget-overlay,.ui-state-disabled,ui-button{background:#fff;border:1px solid #fff;color:#b9cd6d;font-weight:bold} 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. jQuery UI Dialog functionality .ui-widget-overlay,.ui-state-disabled,ui-button{background:#fff;border:1px solid #fff;color:#b9cd6d;font-weight:bold} Perimeter of scalene triangle s = (a + b + c)/2 Here the side length of the triangle mentioned as a,b and c.

 Area of equilateral triangle jQuery UI Dialog functionality .ui-widget-overlay,.ui-state-disabled,ui-button{background:#fff;border:1px solid #fff;color:#b9cd6d;font-weight:bold} area equilateral triangle = (√3/4) a² Here "a" represents the side length of the triangle. jQuery UI Dialog functionality .ui-widget-overlay,.ui-state-disabled,ui-button{background:#fff;border:1px solid #fff;color:#b9cd6d;font-weight:bold} perimeter of area equilateral triangle P = a + b + c Here "a","c" and "c" are representing the side length of the triangle.

 jQuery UI Dialog functionality .ui-widget-overlay,.ui-state-disabled,ui-button{background:#fff;border:1px solid #fff;color:#b9cd6d;font-weight:bold} 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. jQuery UI Dialog functionality .ui-widget-overlay,.ui-state-disabled,ui-button{background:#fff;border:1px solid #fff;color:#b9cd6d;font-weight:bold} Perimeter of sector = L + 2 r Here "L" represents length of arc and "r" represents radius of the sector.

 jQuery UI Dialog functionality .ui-widget-overlay,.ui-state-disabled,ui-button{background:#fff;border:1px solid #fff;color:#b9cd6d;font-weight:bold} Area of circle = Π r² Here "r" represents radius of the circle. jQuery UI Dialog functionality .ui-widget-overlay,.ui-state-disabled,ui-button{background:#fff;border:1px solid #fff;color:#b9cd6d;font-weight:bold} Circumference of circle = 2 Π r Here "r" represents radius of the circle.

 Area of semicircle jQuery UI Dialog functionality .ui-widget-overlay,.ui-state-disabled,ui-button{background:#fff;border:1px solid #fff;color:#b9cd6d;font-weight:bold} Area of Semicircle = (1/2) Π r² Here "r" represents radius of the semicircle. jQuery UI Dialog functionality .ui-widget-overlay,.ui-state-disabled,ui-button{background:#fff;border:1px solid #fff;color:#b9cd6d;font-weight:bold} Perimeter of semicircle = Πr Here "r" represents radius of the semicircle.

 Area of quadrant jQuery UI Dialog functionality .ui-widget-overlay,.ui-state-disabled,ui-button{background:#fff;border:1px solid #fff;color:#b9cd6d;font-weight:bold} Area of quad-rant = (1/4) Π r² Here "r" represents radius of the quadrant.

 jQuery UI Dialog functionality .ui-widget-overlay,.ui-state-disabled,ui-button{background:#fff;border:1px solid #fff;color:#b9cd6d;font-weight:bold} curved surface area of cylinder = 2 Π r h< Here "r" and "h" are representing radius and height of the cylinder. jQuery UI Dialog functionality .ui-widget-overlay,.ui-state-disabled,ui-button{background:#fff;border:1px solid #fff;color:#b9cd6d;font-weight:bold} total surface area of cylinder = 2 Π r (h + r) Here "r" and "h" are representing radius and height of the cylinder. jQuery UI Accordion - Default functionality .ui-widget-overlay,.ui-state-disabled,ui-button{background:#fff;border:1px solid #fff;color:#b9cd6d;font-weight:bold} Volume of cylinder = Π r2h Here "r" and "h" are representing radius and height of the cylinder.

 jQuery UI Accordion - Default functionality .ui-widget-overlay,.ui-state-disabled,ui-button{background:#fff;border:1px solid #fff;color:#b9cd6d;font-weight:bold} Curved surface area of cone = Π r L Here "r" and "L" are representing radius and slant height of the cone. jQuery UI Accordion - Default functionality .ui-widget-overlay,.ui-state-disabled,ui-button{background:#fff;border:1px solid #fff;color:#b9cd6d;font-weight:bold} Total surface area of cone = Π r (L + r) Here "r" and "L" are representing radius and slant height of the cone. jQuery UI Accordion - Default functionality .ui-widget-overlay,.ui-state-disabled,ui-button{background:#fff;border:1px solid #fff;color:#b9cd6d;font-weight:bold} Volume of cone = (1/3)Π r2 h Here "r" and "h" are representing radius and height of the cone.

 jQuery UI Accordion - Default functionality .ui-widget-overlay,.ui-state-disabled,ui-button{background:#fff;border:1px solid #fff;color:#b9cd6d;font-weight:bold} Curved surface area of sphere = 4Π r2 Here "r" represents radius of the sphere. jQuery UI Accordion - Default functionality .ui-widget-overlay,.ui-state-disabled,ui-button{background:#fff;border:1px solid #fff;color:#b9cd6d;font-weight:bold} Volume of sphere = (4/3)Π r3 Here "r" represents radius of the sphere.

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