# 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 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

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 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

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

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

21. Polygon Angle Calculator

22. Circle Sector Area Calculator Apart from the stuff given above if you need any other stuff in math, please use our google custom search here.

If you have any feedback about our math content, please mail us :

v4formath@gmail.com

You can also visit the following web pages on different stuff in math.

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

OTHER TOPICS

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

Featured Categories

Math Word Problems

SAT Math Worksheet

P-SAT Preparation

Math Calculators

Quantitative Aptitude

Transformations

Algebraic Identities

Trig. Identities

SOHCAHTOA

Multiplication Tricks

PEMDAS Rule

Types of Angles

Aptitude Test 