To find the surface area of a rectangular prism, we use the formula:
[tex]\[ \text{Surface Area} = 2(lw + lh + wh) \][/tex]
where:
- [tex]\( l \)[/tex] is the length
- [tex]\( w \)[/tex] is the width
- [tex]\( h \)[/tex] is the height
Given:
- Length ([tex]\( l \)[/tex]) = 7 inches
- Width ([tex]\( w \)[/tex]) = 3 inches
- Height ([tex]\( h \)[/tex]) = 5 inches
Let's go through the computation step by step.
1. First, calculate the area of the three distinct pairs of sides:
[tex]\[ lw = 7 \text{ inches} \times 3 \text{ inches} = 21 \text{ square inches} \][/tex]
[tex]\[ lh = 7 \text{ inches} \times 5 \text{ inches} = 35 \text{ square inches} \][/tex]
[tex]\[ wh = 3 \text{ inches} \times 5 \text{ inches} = 15 \text{ square inches} \][/tex]
2. Now add up these areas:
[tex]\[ lw + lh + wh = 21 \text{ square inches} + 35 \text{ square inches} + 15 \text{ square inches} \][/tex]
[tex]\[ lw + lh + wh = 71 \text{ square inches} \][/tex]
3. Multiply this sum by 2 to get the total surface area:
[tex]\[ \text{Surface Area} = 2 \times 71 \text{ square inches} = 142 \text{ square inches} \][/tex]
Therefore, the surface area of the rectangular prism is:
[tex]\[ 142 \text{ square inches} \][/tex]
