HELPPPPP 2QUESTIONS

#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)

 

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