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# HELPPPPP 2QUESTIONS

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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

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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