Question

The shape of a farm is a quadrilateral. Measurements taken of the farm, by naming its corners as P, Q, R, S in order are as follows. l(PQ) = 170 m, l(QR) = 250 m, l(RS) = 100 m, l(PS) = 240 m, l(PR) = 260 m. Find the area of the field in hectare (1 hectare = 10,000 sq.m).

Answer 1

Area of the field = A(∆PQR) + A(∆PSR) 

In ∆PQR, a = 170 m, b = 250 m, c = 260 m 

Semiperimeter of ∆PQR = s

= 5 x 40 x 60

= 12000 sq.m 

Area of the field = A(∆PQR) + A(∆PSR) 

= 20400 + 12000

= 32400 sq.m 

= 32400/10000 …[1 hectare = 10,000 sq.m] 

= 3.24 hectares 

∴ The area of the field is 3.24 hectares.