Question 1: Calculate the combined area of the three rectangular faces of a prism if each rectangle has dimensions 4 cm by 6 cm.

Answer: 72

Question 2: A rectangular prism has a length of 8 cm, width of 3 cm, and height of 5 cm. Find the total surface area by adding all faces.

Answer: 238

Question 3: Add the areas of the two square faces of a cube with side length 4 cm.

Answer: 32

Question 4: Construct a triangular prism with a rectangular base of 5 cm by 3 cm and a height of 4 cm. Identify and add the areas of its faces.

Answer: Area of rectangle=15 cm², two rectangles=30 cm², two triangles (base 5 cm, height 4 cm)= (1/2)*5*4=10 cm² each, total triangle faces=20 cm², total=15+15+20=50 cm²

Question 5: A triangular prism has two triangular faces each with an area of 6 cm² and three rectangular faces. The rectangular faces are 4 cm by 7 cm, 4 cm by 8 cm, and 4 cm by 5 cm. Add the areas of all faces.

Answer: 6+6+28+32+20=92

Question 6: Identify the mistake: A student added the areas of the rectangular faces (12 cm², 15 cm², 20 cm²) and then added the two triangular faces of a prism as 18 cm² each, getting a total surface area of 83 cm². Correct the error.

Answer: Triangular faces area should be 18 cm² each, total 36 cm²; total surface area=12+15+20+36=83 cm² (correct). The mistake was in the face areas or addition, but the calculation is correct; check face dimensions.

Question 7: A rectangular prism's faces have areas of 24 cm², 36 cm², and 48 cm². Determine the total surface area.

Answer: 108

Question 8: A real-world scenario: A box for storing books has three pairs of faces. The front and back faces are each 30 cm by 40 cm, the sides are 20 cm by 40 cm, and the top and bottom are 30 cm by 20 cm. Add all face areas to find the total surface area of the box.

Answer: Front/back: 2*30*40=2400, Sides: 2*20*40=1600, Top/bottom: 2*30*20=1200, Total=2400+1600+1200=5200 cm²

Question 9: Calculate the total surface area of a composite prism made of a cube (side 3 cm) and a rectangular prism (length 4 cm, width 2 cm, height 3 cm) attached face-to-face.

Answer: Cube faces=6*3²=54; Rectangular prism faces=2*(4*2 + 4*3 + 2*3)=2*(8+12+6)=52; Subtract common face (4*3=12); Total=54+52-2*12=54+52-24=82

Question 10: Challenge: A prism has a square base with side length 5 cm and a height of 10 cm. The rectangular faces are each 5 cm by 10 cm, and the square faces are 25 cm² each. Add all faces to find the total surface area.

Answer: Four rectangular faces=4*5*10=200, two square faces=2*25=50, total=200+50=250 cm²