In a ΔPQR, PQ = PR and the perimeter of ΔPQR is 8(2 + \(\sqrt {2}\)) cm. If the length of QR is \(\sqrt {2}\) times the length of PQ, then find the area of ΔPQR (in cm²) ?

32

ATQ,

PQ = PR = 1 and QR = \(\sqrt {2}\)

Perimeter of ΔPQR = (2 + \(\sqrt {2}\)) unit

⇒ (2 + \(\sqrt {2}\)) unit = 8 (2 + \(\sqrt {2}\)) cm

⇒ 1 unit = 8 cm

⇒ Area of ΔPQR = \(\frac{1}{2}\) × PR × PQ = \(\frac{1}{2}\) × 8 × 8 = 32 cm²