# 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.

## Circle

Area of circle  =  πr2

Circumference of circle  =  2πr

Example problems of area of circle

Example problems of circumference of circle

## Semi Circle

Area of semicircle  =  πr2/2

Circumference of circle  =  πr

Example problems on semi circle

Area of quadrant  =  πr2/4

## Equilateral Triangle

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

Perimeter of equilateral triangle  =  3a

Example problems on equilateral triangle

## Scalene Triangle

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

Area of right triangle  =  (b x h)/2

## Parallelogram

Area of parallelogram  =  b x h

Perimeter of parallelogram =  2(a + b)

Example problems of perimeter of parallelogram

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

Perimeter of quadrilateral  =  a + b + c + d

## Rectangle

Area of rectangle  =  l x w

Perimeter of rectangle  =  2(l + w)

Examples of perimeter of rectangle

## Square

Area of square  =  a x a

Perimeter of square  =  4a

Examples problems on area of square

Examples problems on perimeter of square

## Rhombus

Area of rhombus  =  (d1 x d2)/2

Perimeter of rhombus  =  4a

Examples problems on perimeter of rhombus

## Trapezoid

Area of trapezoid  =  h(a + b)/2

Perimeter of trapezoid  =  a + b + c + d

Examples problems on area of trapezoid

## Sector

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°⋅ πr2

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

Curved surface area of cylinder  =  2πrh

Total surface area of cylinder  =  2πr(h + r)

Volume of cylinder  =  πr2h

## Cone

Curved surface area of cone  =  πrl

Total surface area of cone  =  2πr(l + r)

Volume of cone  =  πr2h/3

## Sphere

Surface area of sphere  =  4πr2

Volume of sphere  =  4πr3/3

## Hemisphere

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

22. Circle Sector Area Calculator

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