Question

1. the surface area of a rectangular prism can be calculated by utilizing the net of the prism as shown below. calculate the total surface area of the rectangular prism.

(there are two figures: one is a rectangular prism with height 15 cm, length 7 cm, width 6 cm; the other is the net of the prism with relevant side lengths marked: 7 cm, 15 cm, 6 cm)
(there is a blank box with unit $cm^2$ at the bottom right)

Explanation:

Step1: Identify face dimensions

The prism has 3 pairs of rectangular faces:

1. Faces with dimensions $7\ \text{cm} \times 6\ \text{cm}$
2. Faces with dimensions $7\ \text{cm} \times 15\ \text{cm}$
3. Faces with dimensions $6\ \text{cm} \times 15\ \text{cm}$

Step2: Calculate area of each pair

• Area of first pair: $2 \times (7 \times 6) = 2 \times 42 = 84\ \text{cm}^2$
• Area of second pair: $2 \times (7 \times 15) = 2 \times 105 = 210\ \text{cm}^2$
• Area of third pair: $2 \times (6 \times 15) = 2 \times 90 = 180\ \text{cm}^2$

Step3: Sum all face areas

$\text{Total Surface Area} = 84 + 210 + 180$

Answer:

$474\ \text{cm}^2$