To determine the surface area of a right rectangular prism with dimensions 4 inches by 5 inches by 6 inches, follow these steps:
1. Understand the formula for the surface area of a rectangular prism:
[tex]\[
\text{Surface Area} = 2(lw + wh + hl)
\][/tex]
where [tex]\( l \)[/tex] is the length, [tex]\( w \)[/tex] is the width, and [tex]\( h \)[/tex] is the height.
2. Identify the dimensions given:
- Length ([tex]\( l \)[/tex]) = 4 inches
- Width ([tex]\( w \)[/tex]) = 5 inches
- Height ([tex]\( h \)[/tex]) = 6 inches
3. Substitute the dimensions into the formula:
[tex]\[
\text{Surface Area} = 2(4 \times 5 + 5 \times 6 + 6 \times 4)
\][/tex]
4. Calculate each of the areas of the individual faces:
- Area of the length and width faces: [tex]\( 4 \times 5 = 20 \)[/tex]
- Area of the width and height faces: [tex]\( 5 \times 6 = 30 \)[/tex]
- Area of the height and length faces: [tex]\( 6 \times 4 = 24 \)[/tex]
5. Sum the areas:
[tex]\[
20 + 30 + 24 = 74
\][/tex]
6. Multiply by 2 (since each pair of opposite faces has the same area):
[tex]\[
2 \times 74 = 148
\][/tex]
Therefore, the surface area of the prism is:
[tex]\[
\boxed{148 \text{ square inches}}
\][/tex]
