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2 years ago

Use Euler’s formula to find the number of vertices in a polyhedron with 6 square faces and 12 edges

Mathematics

1 answer:

Sloan [31]2 years ago

3 0

Answer:

$V = 8$

Step-by-step explanation:

we know that

The Euler's formula state that: In a polyhedron, the number of vertices, minus the number of edges, plus the number of faces, is equal to two

$V - E + F = 2$

in this problem we have

$V=?\\E=12\\F=6$

substitute the given values

$V - 12 + 6 = 2$

solve for V

Combine like terms left side

$V - 6 = 2$

Adds 6 both sides

$V - 6+6 = 2+6$

$V = 8$

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1. 5 in and 1/3 in: Area = 5/3 in^2

2. 5 in and 4/3 in: Area= 20/3 in^2

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Step-by-step explanation:

1. 5 in and 1/3 in

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$Let\\l=5\\w=\frac{1}{3}\\Area=l*w\\=5*\frac{1}{3}\\=\frac{5}{3}\ in^2$

2. 5 in and 4/3 in

Here,

$l= 5\ in\\w=\frac{4}{3}\ in\\Area=l*w\\=5*\frac{4}{3}\\=\frac{20}{3}\ in^2$

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Let

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1. 5 in and 1/3 in: Area = 5/3 in^2

2. 5 in and 4/3 in: Area= 20/3 in^2

3. 5/2 in and 4/3 in: Area=10/3 in^2

4. 7/6 in and 6/7 in: Area = 1 in^2

Keywords: Rectangle, Area

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$\huge\underline{\overline{\mid{\bold{\red{ANSWER}}\mid}}}$

1. Both are corresponding angles, hence they both are equal, so,

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