# CLASS-9PERIMETER & AREA OF QUADRILATERAL

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.

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)]

2

1

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

2

=  (54 X 32) m² = 1728 m²

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