Question

1. milena has a book of paper figures that can be cut out and folded along certain seams to create three - dimensional figures. she cuts out the figure shown below. a. what is the surface area of this figure in square cm? show your work.

Explanation:

Step1: Identify the rectangles

The figure is made up of rectangles.

Step2: Calculate the area of each rectangle

There are 6 rectangles. Two rectangles with dimensions 4 cm by 16 cm, two rectangles with dimensions 4 cm by 20 cm, and two rectangles with dimensions 4 cm by 4 cm.
The area of a rectangle is $A = l\times w$.
For the 4 cm by 16 cm rectangles: $A_1=4\times16 = 64$ $cm^2$, and for two of them the total area is $2\times64 = 128$ $cm^2$.
For the 4 cm by 20 cm rectangles: $A_2=4\times20 = 80$ $cm^2$, and for two of them the total area is $2\times80 = 160$ $cm^2$.
For the 4 cm by 4 cm rectangles: $A_3=4\times4 = 16$ $cm^2$, and for two of them the total area is $2\times16 = 32$ $cm^2$.

Step3: Sum up the areas

The total surface - area $A = 128+160 + 32=320$ $cm^2$.

Answer:

320 $cm^2$