Question

5. Verify Euler's formula after counting the total number of vertices, edges and faces in the figure given at right.​

Answer 1

Answer:

Use the Euler’s Formula (i.e. F +V = E + 2), where F is the total number of Faces in the given solid, V is the total number of the vertices and E is the total number of edges. Count all the faces, vertices and the edges, and to verify the Left-Hand side of Euler’s formula equal to the Right-Hand side of the formula.

Step-by-step explanation:

We know that the Euler’s formula is given as:

F +V = E + 2 where, F is the total number of Faces in the given solid.

V is the total number of the vertices.

E is the total number of edges.

The above given solid is a pyramid whose base is rectangle.

The blue dots in the given figure donates vertices (i.e. corner) of the pyramid.

So, the vertices of the given solid are A, B, C, D, E.

Hence, total number of vertices = 5 = V

Edges of the given solid are AB, BC, CD, AD, DE, AE, BE, CE.

Hence, total number of edges = 8 = E

Now, the faces of the given solid are □ABCD,△ABE,△BCE,△CDE,△ADE◻ABCD,△ABE,△BCE,△CDE,△ADE.

Hence, total number of faces = 5 = F

Now, from Euler’s formula, we know that:

 F +V = E + 2

By putting the value of F, V, E in the above equation, we will get:

⇒5+5=8+2⇒5+5=8+2

⇒10=10⇒10=10

Since, we see that the Left-Hand side of the above equation is equal to the Right-Hand side.

So, Euler’s formula is true for the above given solid.

Hence, verified.

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Answer 2

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