Question

solve this Question ​

Answer 1

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 BC, CD, AD, DE, AE,

Edges of the given solid AB, Hence, total number of edges = 8 = E

Now, the faces of the given solid.

⬜ BCD, ∆ 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

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.

Answer 2

Step-by-step explanation:

verify the euler formula for a pentagonal prism. if a polyhedron is having number of faces as f number of edges as e and the number of vertices as v then the relationship f + v = E + 2 is known ad Euler formula