Question

the figure shows a net for a three - dimensional figure. the net includes three squares. a. what is the three - dimensional figure? b. what is the surface area of the figure? show your work. 1.7 cm 2 cm 2 cm 2 cm 1.7 cm

Explanation:

Step1: Identify the 3 - D figure

The net forms a triangular prism.

Step2: Analyze the components of the surface - area

The surface - area of a triangular prism is the sum of the areas of two triangular faces and three rectangular faces.
The area of a triangle is $A_{triangle}=\frac{1}{2}\times base\times height$. Here, base = 1.7 cm and height = 2 cm, so $A_{triangle}=\frac{1}{2}\times1.7\times2 = 1.7$ $cm^{2}$.
The areas of the three rectangles: Two rectangles have dimensions 2 cm×2 cm and one has dimensions 1.7 cm×2 cm.
The area of a 2 cm×2 cm rectangle is $A_{rect1}=2\times2 = 4$ $cm^{2}$, and there are 2 such rectangles, so their combined area is $2\times4 = 8$ $cm^{2}$.
The area of the 1.7 cm×2 cm rectangle is $A_{rect2}=1.7\times2 = 3.4$ $cm^{2}$.

Step3: Calculate the total surface - area

The total surface - area $A = 2\times A_{triangle}+2\times A_{rect1}+A_{rect2}$.
$A = 2\times1.7+8 + 3.4$.
$A = 3.4+8 + 3.4$.
$A=14.8$ $cm^{2}$.

Answer:

for a:
The three - dimensional figure is a triangular prism.