A (PQRS) = A(∆PSR) + A(∆PQR)
In ∆PSR, l(PS) = 36 m, l(SR) = 15 m
A(∆PSR) = (1/2) x product of sides forming the right angle
= (1/2) x l(SR) x l(PS)
= (1/2) x 15 x 36 = 270 sq.m
In ∆PSR, m∠PSR = 90°
[l(PR)]2 = [l(PS)]2 + [l(SR)]2 …[Pythagoras theorem]
= (36)2 + (15)2 = 1296 + 225
∴ l(PR)2 = 1521
∴ l(PR) = 39m …[Taking square root of both sides]
In ∆PQR, a = 56m, b = 25m, c = 39m
A(PQRS) = A(∆PSR) + A(∆PQR)
= 270 + 420 = 690 sq. m
∴ The area of PQRS is 690 sq.m