Question

A rectangular prism has dimensions of 2 cm by 2 cm by 5 cm. What is its surface area? Explain your reasoning. (Tell what math you did and why.) 2 cm 2 cm 5 cm

Answer 1

$48cm^2$

Explanation

Step 1

to find the total surface area we need to add the area of the six rectangles

Step 1

for rectangle 1 and rectangle 2

$\begin{gathered} \text{rectangle}1=\text{rectangle}2 \\ \text{area}=2\text{ cm }\cdot2cm=4cm^2 \\ \\ \end{gathered}$

now, for rectangles 3 and 4

$\begin{gathered} \text{rectangle}3=\text{ rectangle4} \\ \text{Area}=2\text{ cm}\cdot\text{ 5 cm} \\ \text{Area}=10cm^2 \end{gathered}$

finally, for rectangle 5 and rectangle 6

$\begin{gathered} \text{rectangle}5=\text{rectangle}6 \\ \text{Area}=2\text{ cm}\cdot5\text{ cm} \\ \text{Area}=10cm^2 \end{gathered}$

Step 2

find the total surface area

$\begin{gathered} \text{total}=\text{Arec}1+\text{Arec2}+\text{Arec3}+\text{Arec4}+\text{Arec5}+\text{Arec}6 \\ \text{replacing} \\ \text{total}=4+4+10+10+10+10 \\ \text{total}=48cm^2 \end{gathered}$

I hope this helps you