To calculate the surface area of a rectangular prism, we use the formula:

Question

ScanSolve AI Tutor · Accepted Answer

To calculate the surface area of a rectangular prism, we use the formula:

\text{Surface Area} = 2(lw + lh + wh)

where $l$ is the length, $w$ is the width, and $h$ is the height.

Given:
Base measures 6 cm by 10 cm, so we can take:
Length ( $l$ ) = 10 cm
Width ( $w$ ) = 6 cm
Height ( $h$ ) = 9 cm

Substitute the given dimensions into the formula.
$\text{Surface Area} = 2((10 \text{ cm} \times 6 \text{ cm}) + (10 \text{ cm} \times 9 \text{ cm}) + (6 \text{ cm} \times 9 \text{ cm}))$
Calculate the area of each pair of faces.
$\text{Surface Area} = 2(60 \text{ cm}^2 + 90 \text{ cm}^2 + 54 \text{ cm}^2)$
Sum the areas inside the parentheses.
$\text{Surface Area} = 2(204 \text{ cm}^2)$
Multiply by 2 to get the total surface area.
$\text{Surface Area} = 408 \text{ cm}^2$
The surface area of the prism is $\text{408 cm}^2$ .

Answer