Find the Surface Area of the figure.

Question options:

24 square units

48 square units

88 square units

44 square units



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


 Mar 4, 2018
edited by ForgottenMoon  Mar 4, 2018



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.
\(A_{\text{AGFD}}=24\text{ square units}\) 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.
\(A_{\text{ABCD}}=12\text{ square units}\)  
\(A_{CDFE}=lw\) We might as well find the other one, too.
\(A_{\text{CDFE}}=8\text{ square units}\)  


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.
\(SA_{total}=88\text{ square units}\)  




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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