Question

find the area of shaded region



step by step explaination ....​

Answer 1

By our observation,

△PSQ = Right Triangle at S.

By applying Pythagoras theorem,

PQ² = QS² + PS²

⟹ PQ² = (16)² + (12)² = 256 + 144 = 400

⟹ PQ = √400 = 20 cm

NOW, we know,

Area of triangle = √[s(s - a)(s - b)(s - c)]

Here, s = (20 + 48 + 52)/2 = 60 cm

∴ ar(△PQR) = √[60(60-20)(60-48)(60-52)

= √[60 × 40 × 12 × 8]

= √[6 × 2² × 12 × 8 × 10²]

= 20√[6² × 2⁴] = 20 × 6 × 4

= 20 × 24 = 480 cm²

NOW,

ar(△PSQ) = ½(16)(12) cm²

= 8(12) cm²

= 96 cm²

∴ Shaded Portion = ar(△PQR) - ar(△PSQ)

= 480 cm² - 96 cm²

= 384 cm² (Answer)

@Psyclone