Q4 of 50 Page 12

A park, in the shape of a quadrilateral ABCD, has C=90°, AB = 9 m, BC = 12 m, CD = 5 m and AD = 8 m. How much area does it occupy?

Let consider a quadrilateral ABCD


In ∆BCD;


BD = = 13 m


BC = a = 12 m, CD = b = 5 m, BD = c = 13 m


Let a, b and c are the sides of triangle and s is


the semi-perimeter, then its area is given by:



A = where [Heron’s Formula]


= = 15


A1 =


A1 = = m2


In ∆ABD;


AB = a = 9 m, AD = b = 8 m, BD = c = 13 m


Let a, b and c are the sides of triangle and s is


the semi-perimeter, then its area is given by:


A = where


= = 15


A2 =


A2 = = m2


Therefore area of quadrilateral ABCD = A1 + A2 = 30+35.50 = 65.50 m2


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