Question

Prove that area of the quadrilateral PQRS is 3(4 + 3√3) m2
if PQ = 5m, QR = 5m, RS =
6m, SR= 6 m and diagonal PR = 6 m.

Answer 1

in Quadrilateral PQRS
two ∆ form by diagonal PR are PQR & PSR
in ∆PQR
s = 5+5+6/2=16/2=8
hero's formula
area(∆PQR)=√8(8-5)(8-5)(8-6)
=√8×3×3×2= 12
in ∆PSR
s=6+6+6/2=9
hero's formula
area(∆PRS)=√9(9-6)(9-6)(9-6)
=√9×3×3×3=9√3
area(PQRS)=12+9√3=3(4+3√3)......proved

Answer 2

Answer:

hence the answer is proved