1.

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)= 250m, 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»

Solution :-

PQRS is a quadrilateral. PQ = 170 m, QR 250 m, RS = 100 m, PS = 240 m, PR = 260 m

This question will be solved through Heron's formula of area of TRIANGLE.

There are two triangles in the quadrilateral PQRS.

These are Δ PQR and Δ PSR

In Δ PQR,

PQ = 170 m, QR = 250 m and PR = 260 m

Semi perimeter (s) = (a + b + c)/2

(170 + 250 + 260)/2

⇒ 680/2

s = 340 m

Area of triangle PQR = √340*(340 - 170)*(340 - 250)*(340 - 260)

⇒ √340*170*90*80

⇒ √416160000

⇒ 20400 sq m

In Δ PSR,

SR = 100 m, PS = 240 m and PR = 260 m

S = (a + b + c)/2

⇒ (100 + 240 + 260)/2

⇒ 600/2

⇒ 300 m

Area of triangle Δ PSR = √(300)*(300 - 100)*(300 - 240)*(300 - 260)

⇒ √300*200*60*40

⇒ √144000000

= 12000 sq m

Area of the quadrilateral PQRS = Area of Δ PQR + Area of Δ PSR

⇒ 20400 + 12000

= 32400 sq m

Area in hectares = 32400/10000

= 3.24 hectares

Answer.


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