Question

here are the dimensions of the figures your teammates built. what is the surface area for each figure? match the dimensions to their surface areas. you may wish to create these rectangular figures using your cubes or draw the rectangular sides to help. 1 by 1 by 12 a. 50 units² 1 by 2 by 6 b. 40 units² 1 by 3 by 4 c. 38 units²

Explanation:

Step1: Recall surface - area formula for rectangular prism

The formula for the surface area \(S\) of a rectangular prism with length \(l\), width \(w\), and height \(h\) is \(S = 2(lw+lh + wh)\).

Step2: Calculate surface area for 1 by 1 by 12 prism

Substitute \(l = 1\), \(w = 1\), \(h = 12\) into the formula:
\[

$$\begin{align*} S&=2(1\times1 + 1\times12+1\times12)\\ &=2(1 + 12+12)\\ &=2\times25\\ & = 50\text{ units}^2 \end{align*}$$

\]

Step3: Calculate surface area for 1 by 2 by 6 prism

Substitute \(l = 1\), \(w = 2\), \(h = 6\) into the formula:
\[

$$\begin{align*} S&=2(1\times2+1\times6 + 2\times6)\\ &=2(2 + 6+12)\\ &=2\times20\\ &=40\text{ units}^2 \end{align*}$$

\]

Step4: Calculate surface area for 1 by 3 by 4 prism

Substitute \(l = 1\), \(w = 3\), \(h = 4\) into the formula:
\[

$$\begin{align*} S&=2(1\times3+1\times4 + 3\times4)\\ &=2(3 + 4+12)\\ &=2\times19\\ &=38\text{ units}^2 \end{align*}$$

\]

Answer:

1 by 1 by 12 - a. 50 units²
1 by 2 by 6 - b. 40 units²
1 by 3 by 4 - c. 38 units²