Answer :

Let ABC be a triangle, with BC = 6 cm and angles at its ends are ∠ABC = 40° and ∠ACB = 65° respectively.

Draw AP ⊥ BC, such that APB and APC are right-angled triangles,

Let AP = 'h' cm

BP = 'x' cm and PC = (6 - x) cm

In ΔAPB,

…[1]

In ΔAPC

⇒ 2.1445(6 - x) = h

= h [From 1]

⇒ 12.867 - 2.556h = h

⇒ 3.556h = 12.867

⇒ h = 3.618 cm

Also, area of a triangle

⇒ area(ΔABC) = 3 × 3.618

= 10.854 cm^{2} [appx]

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