PQRS is a quadrilateral in which PQ=5√2cm, QR=5√2cm, RS=8cm, SP=6cm, ∠PSR=

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PQRS is a quadrilateral in which $P Q = 5 \sqrt{2} c m$ , $Q R = 5 \sqrt{2} c m$ , $R S = 8 c m$ , $S P = 6 c m$ , $∠ P S R = ∠ P Q R = 90^{\circ}$ . Then its area is

Options:

A .

40.4 c m^{2}

B .

46.4 c m^{2}

C .

32.4 c m^{2}

D .

49 c m^{2}

Answer: Option D
:
D

Area of right angled triangle $Δ P Q R$
$= \frac{1}{2} \times B a s e \times H e i g h t = \frac{1}{2} \times 5 \sqrt{2} \times 5 \sqrt{2} = 25 c m^{2}$

Area of right angled triangle $Δ P S R$
$= \frac{1}{2} \times 8 \times 6 = 24 c m^{2}$

Area of quadrilateral PQRS
= Area of $Δ P Q R + Δ P S R = 49 c m^{2}$

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