[tex]\large\underline{\sf{Solution-}}[/tex]
Given that,
In triangle TPQ,
As it is given that, RS || PQ
So, it means
⇛∠TRS = ∠TPQ [ Corresponding angles ]
⇛ ∠TSR = ∠TPQ [ Corresponding angles ]
[tex]\rm\implies \: \triangle TPQ \: \sim \: \triangle TRS \: \: \: \: \: \: \{AA \}[/tex]
Now, We know
Area Ratio Theorem,
This theorem states that :- The ratio of the area of two similar triangles is equal to the ratio of the squares of corresponding sides.
[tex]\rm\implies \:\dfrac{ar( \triangle \: TPQ)}{ar( \triangle \: TRS)} = \dfrac{ {PQ}^{2} }{ {RS}^{2} } [/tex]
[tex]\rm\implies \:\dfrac{ar( \triangle \: TPQ)}{15} = \dfrac{ {6}^{2} }{ {3}^{2} } [/tex]
[tex]\rm\implies \:\dfrac{ar( \triangle \: TPQ)}{15} = \dfrac{36 }{9} [/tex]
[tex]\rm\implies \:\dfrac{ar( \triangle \: TPQ)}{15} = 4 [/tex]
[tex]\rm\implies \:ar( \triangle \: TPQ) = 60 \: {cm}^{2} [/tex]
