Question

1. a rectangular prism has dimensions of 2 cm by 3 cm by 4 cm. what is its surface area? explain or show your reasoning.

Explanation:

Step1: Recall surface - area formula

The surface - area formula for a rectangular prism with length $l$, width $w$, and height $h$ is $SA = 2(lw+lh + wh)$.

Step2: Identify the dimensions

Given $l = 4$ cm, $w = 3$ cm, and $h = 2$ cm.

Step3: Calculate $lw$, $lh$, and $wh$

$lw=4\times3 = 12$ cm², $lh = 4\times2=8$ cm², $wh=3\times2 = 6$ cm².

Step4: Calculate the sum inside the parentheses

$lw+lh + wh=12 + 8+6=26$ cm².

Step5: Calculate the surface area

$SA = 2\times26=52$ cm².

Answer:

$52$ cm²