Question

1. what is the surface area of the rectangular prism formed by the pattern below? a. 64 cm² b. 66 cm² c. 128 cm² d. 146 cm². work:

Explanation:

Step1: Identify the three - pairs of faces

A rectangular prism has 6 faces, which come in 3 pairs of equal - area faces. The dimensions of the prism from the net are length $l = 9$ cm, width $w = 5$ cm, and height $h = 2$ cm.

Step2: Calculate the area of each pair of faces

The formula for the surface area of a rectangular prism is $SA=2(lw + lh+wh)$.
For the pair of faces with dimensions $l$ and $w$: $A_1 = 2(lw)=2\times(9\times5)=90$ $cm^2$.
For the pair of faces with dimensions $l$ and $h$: $A_2 = 2(lh)=2\times(9\times2)=36$ $cm^2$.
For the pair of faces with dimensions $w$ and $h$: $A_3 = 2(wh)=2\times(5\times2)=20$ $cm^2$.

Step3: Calculate the total surface area

$SA=A_1 + A_2+A_3=90 + 36+20 = 146$ $cm^2$.

Answer:

D. $146$ $cm^2$