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. consider the figure below. milena folds her figure along the dotted lines to create a three - dimensional shape. b. is this a representation of milenas figure assembled into its three - dimensional shape? explain how you know. c. what is the volume of her figure in cubic centimeters?

Explanation:

Step1: Identify the rectangles and their dimensions

The net consists of rectangles. We have two rectangles with dimensions \(4\times16\), two rectangles with dimensions \(4\times20\) and two rectangles with dimensions \(4\times4\).

Step2: Calculate the area of each - type of rectangle

For a rectangle with length \(l\) and width \(w\), the area \(A = l\times w\).

• Area of \(4\times16\) rectangles: \(A_1=4\times16 = 64\) \(cm^2\), and for two of them \(2A_1 = 2\times64=128\) \(cm^2\).
• Area of \(4\times20\) rectangles: \(A_2 = 4\times20=80\) \(cm^2\), and for two of them \(2A_2=2\times80 = 160\) \(cm^2\).
• Area of \(4\times4\) rectangles: \(A_3 = 4\times4 = 16\) \(cm^2\), and for two of them \(2A_3=2\times16=32\) \(cm^2\).

Step3: Calculate the total surface - area

The total surface area \(S\) of the figure is the sum of the areas of all rectangles. \(S=128 + 160+32=320\) \(cm^2\).

For part B:
No, it is not a representation of Milena's figure assembled into its three - dimensional shape. When we fold the net, the lengths and connections of the rectangles do not match the given three - dimensional figure. In the net, the lengths of the rectangles and their relative positions do not correspond to the solid shown.

For part C:

Step1: Identify the dimensions of the rectangular prism

When folded, the rectangular prism has length \(l = 20\) \(cm\), width \(w = 4\) \(cm\) and height \(h = 4\) \(cm\).

Step2: Use the volume formula for a rectangular prism

The volume formula for a rectangular prism is \(V=l\times w\times h\).
\(V = 20\times4\times4=320\) \(cm^3\).

Answer:

A. \(320\) \(cm^2\)
B. No. When we fold the net, the lengths and connections of the rectangles do not match the given three - dimensional figure.
C. \(320\) \(cm^3\)