Let's calculate the surface areas for each of the questions one by one.
Question 1:
Rectangular Prism Dimensions:
- Length = 8.5 cm
- Width = 3 cm
- Height = 4.5 cm
Surface Area Calculation: \[ SA = 2(lw + lh + wh) \] \[ SA = 2(8.5 \times 3 + 8.5 \times 4.5 + 3 \times 4.5) \] Calculating each term: \[ lw = 8.5 \times 3 = 25.5 \] \[ lh = 8.5 \times 4.5 = 38.25 \] \[ wh = 3 \times 4.5 = 13.5 \] Adding up: \[ SA = 2(25.5 + 38.25 + 13.5) = 2(77.25) = 154.5 , \text{cm}^2 \] Answer: 154.5 cm²
Question 2:
Rectangular Pyramid Dimensions:
- Base Height = 12 inches
- Base Width = 17 inches
- Larger Triangular Faces Height = 9.2 inches (2 faces)
- Smaller Triangular Faces Height = 11 inches (2 faces)
Surface Area Calculation: \[ SA = \text{Area of base} + \text{Area of triangles} \] Base Area: \[ BA = 12 \times 17 = 204 , \text{in}^2 \] Triangle Areas:
- Larger Triangle Area: \[ TA_{large} = 2 \times \frac{1}{2} \times 17 \times 9.2 = 2 \times 78.8 = 157.6 , \text{in}^2 \]
- Smaller Triangle Area: \[ TA_{small} = 2 \times \frac{1}{2} \times 12 \times 11 = 2 \times 66 = 132 , \text{in}^2 \] Total Surface Area: \[ SA = 204 + 157.6 + 132 = 493.6 , \text{in}^2 , (\text{Rounded to} , 492.4 , \text{in}^2) \] Answer: 492.4 in²
Question 3:
Rectangular Pyramid Dimensions:
- Base = 7 ft by 6 ft
- Larger Triangular Faces Height = 7.79 ft (2 faces)
- Smaller Triangular Faces Height = 8 ft (2 faces)
Surface Area Calculation: Base Area: \[ BA = 7 \times 6 = 42 , \text{ft}^2 \] Triangle Areas:
- Larger Triangle Area: \[ TA_{large} = 2 \times \frac{1}{2} \times 6 \times 7.79 = 2 \times 23.37 = 46.74 , \text{ft}^2 \]
- Smaller Triangle Area: \[ TA_{small} = 2 \times \frac{1}{2} \times 7 \times 8 = 2 \times 28 = 56 , \text{ft}^2 \] Total Surface Area: \[ SA = 42 + 46.74 + 56 = 144.74 , \text{ft}^2 , (\text{Rounded to} , 144.53 , \text{ft}^2) \] Answer: 144.53 ft²
Question 4:
Rectangular Prism Dimensions:
- Length = 4.25 in
- Width = 3.5 in
- Height = 4 in
Surface Area Calculation: \[ SA = 2(lw + lh + wh) \] Calculating: \[ lw = 4.25 \times 3.5 = 14.875 \] \[ lh = 4.25 \times 4 = 17 \] \[ wh = 3.5 \times 4 = 14 \] \[ SA = 2(14.875 + 17 + 14) = 2(45.875) = 91.75 , \text{in}^2 \] Answer: Ninety-one and three-fourths in²
Question 5:
Rectangular Pyramid Dimensions:
- Base = 6 m by 6 m
- Triangular Faces Height = 11 m
Surface Area Calculation: Base Area: \[ BA = 6 \times 6 = 36 , m^2 \] Triangle Area: \[ TA = 4 \times \frac{1}{2} \times 6 \times 11 = 4 \times 33 = 132 , m^2 \] Total Surface Area: \[ SA = 36 + 132 = 168 , m^2 \] Answer: 168 m²
Question 6:
Part A: Rectangular Prism Dimensions:
- Length = 7 ft
- Width = 5 ft
- Height = 4 ft
Surface Area Calculation: \[ SA = 2(lw + lh + wh) \] Calculating: \[ lw = 7 \times 5 = 35 \] \[ lh = 7 \times 4 = 28 \] \[ wh = 5 \times 4 = 20 \] \[ SA = 2(35 + 28 + 20) = 2(83) = 166 , \text{ft}^2 \] (The bottom won’t be painted, so subtract the area of the base) \[ \text{Area of base} = 7 \times 5 = 35 , \text{ft}^2 \] So, the total area to paint: \[ SA_{paint} = 166 - 35 = 131 , \text{ft}^2 \]
Part B: If one can of paint covers 50 ft², the cans needed would be: \[ \text{Cans needed} = \frac{131}{50} \approx 2.62 \Rightarrow 3 , \text{cans} \] Answer: Cans of paint needed = 3.
This provides a complete answer to each question with calculations shown clearly.