Mensuration Formulas For all 2D Shapes and 3D Shapes

Mensuration is the branch of mathematics which involves the geometrical shapes which may be 2D, 3D and their perimeter, area, surface area and volume with many of their measurements.

The 2-dimensional shapes are those which are having only two parameters length and breadth. While the 3-dimensional shapes are the shapes having length, breadth and also height.

In this article we see all the measurement formulae of all the geometrical shapes. It helps in solving the problems of geometry based on mensuration. Here we go from basic and use these formulae in daily life also.

Perimeter:

  • Perimeter is not only related to the geometrical things but in our daily life also sometime we have to know the perimeter. So what is this perimeter?
  • Perimeter is the length of the path of any object in two dimension or it is the outline of that object.
  • It is measured in meter.

Area:

  • In geometry, area is the space occupied by particular object or shape. The different shapes are having different areas. In our day-to-day life we come across many conditions like building construction, cloth stitching, in colouring also in which we want to know approximate areas of objects so that we can easily solve this type of problems.
  • The two-dimensional object has area while the three-dimensional object has surface area.
  • The area and surface area are measured in square units like meter square, feet square etc.

Volume:

  • Every three-dimensional object possesses volume in space. Volume is space occupied by the object in three dimensions. According to the dimension of body it occupies the different volumes.
  • In real life we daily go through the concepts of volume. There are some specific geometrical shapes like cube, cone, cylinder, sphere which are having their fixed volume. By using these basic shapes volume, we can find the volume of any body.
  • Volume is measured in cubic units i.e., meter cube, centimeter cube or in litre also.
  • Not only solids, but also liquids and gases possesses volume in which shape of object we have poured them.

Mensuration Formulas For all 2D Shapes

1.) Rectangle:

  • Perimeter of rectangle = 2* (a + b)
  • area of rectangle =2* length*breadth = 2* (a * b)

2.) Square:

  • Perimeter of square = 4*side of square = 4*a
  • Area of square = square of side = a2

3.) Circle:

  • Perimeter of circle = 2*π* r
  • Area of circle = π* r2

4.) Semicircle:

  • Perimeter of semicircle= π*r
  • Area of semicircle= ½ (π*r2)

5.) Triangle:

  • Perimeter of triangle = a + b + c
  • Area of triangle = ½ * base* height

6.) Equilateral triangle:

  • Perimeter of equilateral triangle = 3* a
  • Area of equilateral triangle = √3/4 * a2

7.) Isosceles triangle:

  • Perimeter of isosceles triangle = 2*a + b
  • Area of isosceles triangle = ½ * base*height = ½*b*h
  • Area of right-angled isosceles triangle = ½ *base * height = ½ *a*a= ½*a2

8.) Parallelogram:

  • Perimeter of parallelogram = 2* (a + b)
  • Area of parallelogram = base*height= DC*AE

9.) Rhombus:

  • Perimeter of rhombus = 4* a
  • Area of rhombus = ½ * product of two diagonals

10.) Trapezoid:

  • Perimeter of trapezoid = a + b + c + d
  • Area of trapezoid = ½ *(sum of parallel sides)

11.) Regular hexagon:

  • Perimeter of regular hexagon = 6* a
  • Area of regular hexagon = 3√3/2* a2

12.) Regular pentagon:

  • Perimeter of regular pentagon = 5* a
  • Area of regular pentagon = 5/2 * s* a

Mensuration Formulas For all 3D Shapes

Following are somethree-dimensional geometrical shapes with their surface areas:

1.) Cube:

  • Surface area of cube = 6*a2
  • Volume of cube = a3
  • Curved surface area= 4*a2

2.) Cuboid:

  • Surface area of cuboid = 2(l*b + b*h + l*h)
  • Volume of cuboid = l*b*h
  • Curved surface area = 2h*(l + b)

3.) Cylinder:

  • Surface area of cylinder = perimeter of circular base*(radius + height) = 2πr*(r + h)
  • Volume of cylinder = area of spherical base*height= π*r2*h
  • Curved surface area = 2π*r*h

4.) Cone:

  • Surface area of cone = π*r(l + r)
  • Volume of cone = 1/3 π*r2*h
  • Curved surface area of cone = π*r*l

5.) Sphere:

  • Surface area of sphere = 4*π*r2
  • Surface area of hemisphere = 3* π*r2
  • Volume of sphere = 4/3*π*r3
  • Volume of hemisphere = 2/3* π*r3
  • Curved surface area of sphere = 4πr2
  • Curved surface area of hemisphere = 2πr2

Updated: September 8, 2021 — 3:57 pm

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