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Find the Surface Area of the figure.

Question options:

24 square units

48 square units

88 square units

44 square units

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Which angle has the same measure of the dihedral angle formed by the green face and the purple rectangle?

Question  options:

Angle JAB

Angle HAJ

Angle JAE

Angle JDC

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 Mar 4, 2018
edited by ForgottenMoon  Mar 4, 2018
 #1
avatar+2421 
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#1) 

 

One way to approach this problem is to add up the sides of all the faces. All the faces are rectangular-shaped, so finding their individual area is not too difficult.

 

\(A_{\text{AGFD}}=lw\) This is the formula for the area of this side. Its length (l) is 6 units, and the width (w) is 4 units.
\(A_{\text{AGFD}}=6*4\)  
\(A_{\text{AGFD}}=24\text{ square units}\) Area is always represented as a square unit since it measures in two dimensions. 
   

 

We can do the same calculation for the other faces.

 

\(A_{\text{ABCD}}=lw\) Use the diagram to find these lengths.
\(A_{\text{ABCD}}=6*2\)  
\(A_{\text{ABCD}}=12\text{ square units}\)  
   
\(A_{CDFE}=lw\) We might as well find the other one, too.
\(A_{\text{CDFE}}=4*2\)  
\(A_{\text{CDFE}}=8\text{ square units}\)  
   

 

Because the above figure is a rectangular prism, the opposite face is equal to one that I already found. 

 

\(SA_{total}=2(A_{\text{AGFD}}+A_{\text{ABCD}}+A_{\text{CDFE}}\) Let's plug in the values we know.
\(SA_{total}=2(24+12+8)\) One luxury unique to addition and multiplication is that you can perform the calculation in any order you desire; therefore, I will find the sum of 12 and 8 because they add up to a number where its last digit is zero.
\(SA_{total}=2(24+20)\)  
\(SA_{total}=2(44)\)  
\(SA_{total}=88\text{ square units}\)  
   

 

#2)

 

dihedral angle is formed when two planes intersect. \(\angle JAB\) has the same measure because it is included in the dihedral angle. 

 Mar 4, 2018

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