Question

the dimensions of a rectangular prism are shown. h = 12 cm / = 14 cm w = 10 cm what is the surface area of the prism? 133 cm² 144 cm² 856 cm² 1680 cm²

Explanation:

Step1: Recall surface - area formula

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

Step2: Substitute the given values

Given $l = 14$ cm, $w = 10$ cm, and $h = 12$ cm. First, calculate $lw$: $lw=14\times10 = 140$ $cm^{2}$. Then, calculate $lh$: $lh = 14\times12=168$ $cm^{2}$. Next, calculate $wh$: $wh=10\times12 = 120$ $cm^{2}$.

Step3: Calculate the sum inside the parentheses

$lw+lh + wh=140 + 168+120=428$ $cm^{2}$.

Step4: Multiply by 2

$SA = 2\times428=856$ $cm^{2}$.

Answer:

C. $856$ $cm^{2}$