Question

find the surface area of the rectangular prism (above) using its net (below).

Explanation:

Step1: Identify face areas

A rectangular prism has 6 faces. The pairs of opposite - faces have equal areas. The three different face - areas are calculated as follows.
For the face with dimensions 4 and 3: $A_1 = 4\times3=12$; for the face with dimensions 4 and 2: $A_2 = 4\times2 = 8$; for the face with dimensions 3 and 2: $A_3=3\times2 = 6$.

Step2: Calculate surface area

The surface area $S$ of a rectangular prism is given by $S = 2(A_1+A_2 + A_3)$.
Substitute $A_1 = 12$, $A_2 = 8$, and $A_3 = 6$ into the formula:
$S=2(12 + 8+6)$.
First, calculate the sum inside the parentheses: $12 + 8+6=26$.
Then, multiply by 2: $S = 2\times26=52$.

Answer:

52