12. In the given figure, RS is parallel to PQ, If RS = 3 cm, PQ = 6 cm and ar(∆TRS) = 15cm³, then ar (∆TPQ) = ? (a) 70 cm² (b) 58 cm² (c) 60 cm² (d) 64 cm²

Given that,

In triangle TPQ,

RS || PQ, RS = 3 cm, PQ = 6 cm, ar(∆ TRS) = 15 sq. cm

As it is given that, RS || PQ

So, it means

⇛∠TRS = ∠TPQ [ Corresponding angles ]

⇛ ∠TSR = ∠TPQ [ Corresponding angles ]

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.

If you start with all the sides of the hexagon being congruent, you can then figure out angle measures, then you can conclude that all the sides of polygon GBHE are congruent, so it is a rhombus.
Each angle at vertices H and G measures 120 deg.
Each angle at vertices E and B measures 60 deg.