Answer:
Total surface area = 434 cm²
Total volume = 470 cm³
Step-by-step explanation:
1. The prism can be decomposed into two rectangular prisms which are the bigger rectangular prism and the smaller rectangular prism
✔️Total surface area of the prism = (surface area of the bigger prism - area of the face joined to the smaller prism) + (surface area of the smaller prism - area of the face joined to the bigger prism)
Surface Area of bigger prism = 2(LW + LH + HW)
L = 10 cm
H = 8 cm
W = 9 - 5 = 4 cm
Area of bigger rectangular prism = 2(10*4 + 10*8 + 8*4)
= 304 cm²
Surface area of the smaller prism = 2(LW + LH + HW)
L = 10 cm
H = 3 cm
W = 5 cm
Area of bigger rectangular prism = 2(10*5 + 10*3 + 3*5)
= 190 cm²
Area of the face joining both rectangular prisms = L*W
L = 10 cm
W = 3 cm
Area = 10*3 = 30 cm²
✅total surface area of the prism = (304 - 30) + (190 - 30) = 274 + 160 = 434 cm²
2. Volume of the prism = volume of the bigger rectangular prism + volume of the smaller rectangular prism
✔️Volume of the bigger rectangular prism = L*W*H
L = 10 cm
H = 8 cm
W = 9 - 5 = 4 cm
Volume = 10*8*4 = 320 cm³
✔️✔️Volume of the bigger rectangular prism = L*W*H
L = 10 cm
H = 3 cm
W = 5 cm
Volume = 10*3*5 = 150 cm³
✅Total Volume of the prism = 320 + 150 = 470 cm³
