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Look at the measures shown in the given figure and find the area of PQRS.

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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)= 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

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