CLASS-9
PERIMETER & AREA OF QUADRILATERAL

PERIMETER & AREA OF QUADRILATERALS –

i) Perimeter of a Quadrilateral –

If A, B, C, and D are the lengths of the four sides of a quadrilaterals, then its perimeter = A + B + C + D

ii) Area of a Quadrilateral –

a) When one diagonal and perpendiculars from remaining vertices to the diagonal are given.

Area of quadrilateral- 

ABCD = area △ABD + area △BCD

         1                       1

    = ------ X BD X AL + ------ X BD X CM

         2                       2

         1

    = ----- BD (AL + CM)

         2

      1

 = ----- X one diagonal X sum of lengths of perpendiculars on it from

      2

maintaining vertices.


There are some example is given below for your better understanding -

Example.) In a four sided field, the longer diagonal is 110 m. The lengths of the perpendiculars from the opposite vertices upon this diagonal are 18.6 m and 13.4 m respectively. Find the area of the field.

Ans.) Let ABCD be the field and AC be its longer diagonal.

Let, BL ⊥ AC and DM ⊥ AC such that

AC = 110 m, BL = 18.6 m and DM = 13.4 m

                              1

So, area of the field = [------ X AC X (BL + DM)] m²

                              2

                             1

                       = [------ X 108 X (18.6 + 13.4)] m²

                             2

                       =  (54 X 32) m² = 1728 m²  

So, the area of the field is 1728 m² (Ans.)