Mensuration

3.  Mensuration

3.1 – Area

  • Area of a Rectangle:
  • Length × Width
  • l × w
  • Area of  Trapezium:
  • ½ (Base+ Base2) × Height
  • ½ (a + b) h
  • Area of a Kite:
  • ½ (Diagonal1 × Diagonal2)  
  • ½ (a × b)
  • Area of a Triangle:
  • ½ (Base × Height)
  • ½ (b × h)

OR

  • ½ (a × b) sin C          
  • Area of a Parallelogram:
  • Base × Height
  • b × h

OR

  • (b × a) sin  theta    
  • Area of a Parallelogram:
  • Base × Height
  • b × h

OR

  • (b × a) sin  theta

3.2 – The Circle

  • Circumference of a Circle:
  • Circumference = π × diameter

                    which is  πd

OR

  • Circumference = 2 × π × radius

                      which is   2πr

  • Area of a Circle:
  • Area = π × radius²

           which is  πr²

3.3 – Arc Length and Sector Area

Arc Length:

Arc Length =    theta/360 × 2 × π × radius

                               which is theta/360 × 2πr

  • Sector Area = ᶿ/360 × π × radius²

                    which is  theta/360 × πr²

3.4 – Volume

  • Volume of a Prism:
  • Volume of a Prism = (area of cross section) × length

              which is  A × l

  • Volume of a Cylinder:
  • Volume of a Cylinder = (area of cross section) × length
  • Volume of a Cylinder = π × radius² × height

              which is  πr²h

  • Volume of a Pyramid:
  • Volume of a Pyramid = 1/3 × (base area) × height

                  which is 1/3 × (A) × h

  • Volume of a Cone:
  • Volume of a Cone = 1/3 × π × radius² × height

           which is 1/3 πr²h

  • olume of a Sphere:
  • Volume of a Sphere = 4/3 × π × radius³

       which is  4/3 πr³

3.5 – Surface Area

  • Cylinder:
  • Curved Surface Area = 2 × π × radius × height

                               2πrh

  • Total Surface Area = (2 × π × radius × height) + (2 × π × radius²)

                                  2πrh + 2πr²

  • Sphere:
  • Surface Area = 4 × π × radius²

                      4πr²

  • Cone:
  • Curved Surface Area = π × radius × slant height

                                      πrl

  • Total Surface Area = (π × radius × slant height) + (π × radius²)

                                   πrl + πr²                                                 

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