Questions: Find the surface area of this rectangular prism. Be sure to include the correct unit in your answer. 1 cm 7 cm 2 cm cm cm^2

Transcript text: Find the surface area of this rectangular prism. Be sure to include the correct unit in your answer. $1\text{ cm}$ $7\text{ cm}$ $2\text{ cm}$ cm $\text{cm}^2$

Solution

Solution Steps

Step 1: Identify the dimensions of the rectangular prism

The given rectangular prism has the following dimensions:

Length (l) = 7 cm
Width (w) = 3 cm
Height (h) = 4 cm

Step 2: Write the formula for the surface area of a rectangular prism

The surface area (SA) of a rectangular prism is given by the formula: \[ SA = 2lw + 2lh + 2wh \]

Step 3: Substitute the dimensions into the formula

Substitute the given dimensions into the formula: \[ SA = 2(7 \, \text{cm} \times 3 \, \text{cm}) + 2(7 \, \text{cm} \times 4 \, \text{cm}) + 2(3 \, \text{cm} \times 4 \, \text{cm}) \]

Step 4: Calculate each term

Calculate each term separately: \[ 2(7 \times 3) = 2 \times 21 = 42 \, \text{cm}^2 \] \[ 2(7 \times 4) = 2 \times 28 = 56 \, \text{cm}^2 \] \[ 2(3 \times 4) = 2 \times 12 = 24 \, \text{cm}^2 \]

Step 5: Sum the calculated terms

Add the calculated terms to find the total surface area: \[ SA = 42 \, \text{cm}^2 + 56 \, \text{cm}^2 + 24 \, \text{cm}^2 = 122 \, \text{cm}^2 \]