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