Question

what is the surface area of the box formed by the pattern below?
a. $1,360\\ \text{m}^2$
b. $972\\ \text{m}^2$
c. $772\\ \text{m}^2$
d. $146\\ \text{m}^2$

Explanation:

Step1: Identify the dimensions of the box

From the net, we can see that the length \( l = 17\) m, width \( w = 10\) m, and height \( h = 8\) m.

Step2: Recall the formula for the surface area of a rectangular prism (box)

The formula for the surface area \( SA \) of a rectangular prism is \( SA = 2(lw + lh + wh) \).

Step3: Substitute the values into the formula

First, calculate \( lw \), \( lh \), and \( wh \):

• \( lw = 17\times10 = 170\)
• \( lh = 17\times8 = 136\)
• \( wh = 10\times8 = 80\)

Then, substitute these into the surface area formula:
\( SA = 2(170 + 136 + 80) \)

Step4: Simplify the expression inside the parentheses

\( 170 + 136 + 80 = 386 \)

Step5: Multiply by 2

\( SA = 2\times386 = 772 \)

Answer:

C. \( 772\space m^{2} \)