Question

Need help please answering this problem!!

Answer 1

NR = NS + SR = 18 + 45 = 63 m

If NPS~NQR then we can find QR:
$\frac{PS}{QR}= \frac{NS}{NR} \ \to \ \frac{7.2}{QR}= \frac{18}{63} \ \to \ \\ QR= \frac{63*7.2}{18}= 25.2 \ m$

$\text{Area}_{PQRS} = \text{Area}_{NQR}-\text{Area}_{NPS} \\ \\ \text{Area}_{NQR}= \frac{NR*QR}{2} = \frac{63*25.2}{2}= 793.8 \ m^2 \\ \\ \text{Area}_{NPS}= \frac{NS*PS}{2} = \frac{18*7.2}{2}= 64.8 \ m^2 \\ \\ \text{Area}_{PQRS} =793.8 - 64.8 = 729 \ m^2$

Answer: C.