Question

A field is in the shape of a quadrilateral ABCD in which side AB = 18 m, side AD = 24 m, side BC = 40m, DC = 50 m and angle A = 90°. Find the area of the field.

Answer 1

Since ∠A = 90°
By Pythagorus Theorem,
In ∆ABD,

Now, the area of ΔABD = `1/2 (18)(24)`

= (18) (12) = 216 m²

In ΔABD

BD = `sqrt("AB"^2 + "AD"^2) = sqrt(18^2 + 24^2)`

= `sqrt(324 + 576) = sqrt(900) = 30`m.

S = `120/20 = 60 cm^2`

 =`sqrt( 60xx10xx20xx30)`

= `sqrt(10xx2xx3xx10xx10xx2xx10xx3)`

= 10 × 10 × 6

= 600 cm²

Area of quadrilateral ABCD

= 816cm²