Vertices of rectangular pool are A(3,2),B(7,8),C (4,10), and D (0,4).
AB=[tex]\sqrt{(7-3)^{2}+(8-2)^{2}}= \sqrt{16+36}=\sqrt{52}[/tex] yard=CD
BC=[tex]\sqrt{(7-4)^{2}+(8-10)^{2}}=\sqrt{9+4}=\sqrt{13}[/tex] yard=DA
Area of rectangular pool=Length × Breadth
=√52 ×√13=13×2=26 square yard
Vertices of triangle are P(5,2),Q(7,2) and R(7,5).
PQ= 2 units, QR= 3 units
Area of right triangle PQR= [tex]\frac{1}{2}[/tex]×PQ×PR
=[tex]\frac{1}{2}[/tex]×2×3= 3 square yards
Total material needed to cover bot rectangular pool and triangular hot tub= Area of rectangle + Area of right triangle=26+3=29 square yards
